Transcript for:
Temperature and Heat Overview

good morning everybody today we will continue with temperature and heat very important for engineering and also for basic science and also very important for industrial applications so usually if you are doing something you should know what is the temperature at that conditions and today we will discuss how to use different temperature measurement systems and we will discuss the relation between temperature and heat so we will learn the meaning of thermal equilibrium and what thermometers really measure we will discuss different types of thermometers and we will discuss the physics behind the absolute or calvin temperature scale we have different temperatures case we will discuss them and then we will learn how the dimensions of an object change as a result of a temperature change this is thermal expansion or tamil shrinking so the shape of the object changes as a function of temperature this is also very important for industrial applications for engineering applications and in the next part we will learn how to do calculations that involve heat flow temperature changes and changes of phase and finally we will finish how heat is transferred by conduction convection and radiation so with this one we will finish this chapter let me start with the temperature and tamil equilibrium we use thermometers to measure temperature here on the right side you see a thermometer very common one and within the thermometer we have a volume within this volume there is a liquid it can be mercury or ethanol okay in addition to that this thermometer is made from thin glass wall why it is required for the thermal equilibrium for fast thermal equilibrium and here we have thin glass wall in this part but here we have thick glass wall you see the wall of this part is thicker and we have capillary of small volume here so if you put here a heat source then the temperature of this liquid here will increase and then the volume of this liquid within this thermometer will increase then you will have nev level here and this part will also be filled or if you use a cooling source close to here then this level of the temperature will decrease it will come somewhere here because due to the cooling the volume of this material within this thermometer will decrease so this is the general working principle of glass thermometer but here we have very important term thermal equilibrium so you would like to measure the temperature of some object or body then you use this thermometer so let's consider that here there is a body okay or here there is an object and this thermometer and this object are very close contact they touch to each other okay so this has certain temperature t1 and this thermometer the liquid within the thermometer has t2 okay before they touch to each other and after certain time if they touch each other after certain time t1 will be equal to t2 okay so this is the thermal equilibrium and then the temperature of the liquid within this thermometer will be equal to the temperature of the body here on the left side and then if the temperature on the left side t1 is higher than the volume of this liquid within the thermometer will increase and then the temperature within the temperature scale you can read the actual temperature of the body and let me discuss gas thermometer so this is a container of gas at constant volume here we have a container okay it has constant volume its volume cannot change okay and we have a gas within this volume and if you use a heat source if you increase the temperature of this gas within the container then the pressure of this gas will increase and here we have a pressure gauge okay you measure the pressure and this pressure you read on the gauge is proportional to the temperature of the gas so you can use the container of gas to measure the temperature so changes in temperature cause the pressure of the gas to change do you have any questions here and we have very common thermometers used in industry used in engineering and also used for scientific purposes here we have platinum thermometers and here we have serenox thermometers this upper part belongs to the platinum thermometers platinum is a metal okay and metals have this type of behavior with the temperature this is the temperature in kelvin and this is the resistance or resistivity of the material okay and in case of metals there is this type of behavior so what do you see here when you increase the temperature here on the right side we have a region which is very sensitive to the temperature you increase the temperature then resistivity increases you increase the temperature then resistivity increases okay here at low temperatures let's consider this is the zero kelvin and this is let's say thousand kelvin okay at low temperatures this thermometers this metal thermometers are not so sensitive to the temperature okay so you increase the temperature but resistivity does not change so much here resistivity does not change so much but at high temperatures metal thermometers platinum thermometers are very sensitive to the change in the temperature so these are the different platinum thermometers from lakeshore one of the main temperature sensor producer and temperature controller producer in the world and we have few of them in our laboratory and here you see a common resistance versus temperature graph of this thermometers what do you see here this is let's say around 30 kelvin something like this and here you see 10 kelvin okay and in this region the sensor the platinum is not sensitive to the temperature changes but at high temperatures they are very sensitive to the change in the temperatures so here we have 100 kelvin and we have this resistance here we have many 100 kelvins and here we have this resistance okay so by measuring the resistance you can get the idea about the temperature you can measure the temperature so what do you see here in reality within this part there is this type of coil made from the platinum and we measure the resistance of this platinum as a function of temperature okay so resistance gives us information about the temperature of the system these are also called as resistance thermometers okay and in cernox thermometers semiconductors are used okay and semiconductors have different temperature relation this is the resistance of the semiconductor let me clean the upper part and then you will better see the difference in between this is the resistance versus temperature curve for metals and as i told you they are very sensitive at high temperatures and in case of semiconductor thermometers at high temperatures they are not so sensitive to the temperature changes but at low temperatures semiconducting sensors are very sensitive to the small changes in the temperature okay so here for example you cool the sample down to this temperature and you have this resistance and if you further call the sample down to this temperature then we have this resistance so we have huge resistance change in the ceramics thermometers in semiconducting thermometers and there are different shapes in the cenox thermometers again you measure the resistance from this arms you measure the resistance from this arms okay there are different types of designs here we have again resistance versus temperature curve for cernox thermometers and depending on the thermometer type here you see different cernox numbers produced by lakeshore they have different resistance versus temperature behavior what do you see here at low temperatures they have huge change in their resistance due to the temperature but at high temperatures the change in the resistance as a function of temperature decreases so these are the metal and semiconducting thermometers and by using these thermometers you can measure the temperature so we are talking about temperature we are talking about thermometers and these are also thermometers widely used in industry very important very stable thermometers and there are also infrared thermometers these thermometers includes an infrared detector here within the thermometer okay and you don't need to touch to the system so in case of this glass thermometers so this body here should touch to the thermometer in case of this container body should touch this thermometer in case of this metal and semiconductor detectors body should touch to the thermometer but in case of infrared detectors infrared thermometers touching is not necessary okay this thermometers can measure from far from the body okay so i will go into detail related to the working principles of this thermometers but they are also very widely used for everyday life and class is infrared thermometers another type of thermometer is a bi-metallic strip here in picture a we have a bi-metallic strip made from two metals this is the metal one on top okay and at the bottom there is another metal but there are different metals okay there's different properties with different thermal properties so if you use a heat source here if you heat the material then this bottom metal metal two will expand and this upper metal metal one blue one will also expand but since they have different thermal expansion properties then you will have this type of shape and you can measure the temperature by using this type of bi-metals and here there is a thermometer on the right side a spring spiral spring made from a bi-metal used here within this thermometer okay so we have a scale here in degree celsius you see from 0 to 100 degrees celsius and here we have we have a pointer and this pointer is attached to a spring and this spring made from bimetallic strip then as a function of temperature to the tamil expansion the shape of the spring changes and then you can measure the temperature by using this bi-metallic strip this is another type of thermometer and with this one i finished the types of thermometers so depending on the application you can use these thermometers do you have any question up to this point now let me discuss the thermal equilibrium what is thermal equilibrium this is the xerox law of thermodynamics and it is related to the tamil equilibrium here in picture a we have a system a or material a okay and here on the right side we have system b or material b and at the bottom we have system c or material c and between system a and b we have an insulator let me use another pen color here we have an insulator this is thermal insulator okay so this material is used to insulate these two systems okay system a and b so this system has certain temperature ta this system has certain temperature tb on the right side and system c has also certain temperature okay and here let me use another color we have thermal conductor okay between system a and system c we have tamil conductor so this system a and c can interact family very well okay because here we have thermal conductor and between system b and system c there is also a thermal conductor okay so heat transfer can happen easily between b and c systems also between a and c systems but between a and b we have a thermal insulator and heat transfer is block you can see okay so if systems a and b are each in thermal equilibrium with system c so what i have told you that let me use another color here here we have on the left side system a at the bottom here we have system c and these two systems system a and system c are in tamil equilibrium because there is a thermal conductor in between okay and they are in thermal equilibrium what is the meaning of that ta is equal to tc and here on the right side the system b and system c are also in thermal equilibrium okay so here we have a conductor okay thermal conductor so they are in equilibrium it means that tb is equal to tc then if a and c and b and c are in thermal equilibrium then i can write that this one t a and t b are equal to each other they are also in tamil equilibrium okay look at this system look at this one here on the right side here we have a thermal conductor between a and b this is the on the left side system a with ta and on the right side we have system b with temperature tb and here we have system c with temperature c okay so if this two systems system a and system c are in thermal equilibrium and these two systems system b and c are in thermal equilibrium then it means that this a and b are in thermal equilibrium so actually here i should talk about also the thermal conductors thermal insulators so thermal conductivity of each material is unique okay so different materials have different tamil conductivity and thermal insulating properties if you have a perfect insulator okay just consider that you have a perfect thermal insulator it means that there is no heat transfer between two systems okay because here we have a thermal barrier okay so we will go into detail with this one so this is the zeroth love of thermodynamics it talks about the thermal equilibrium do you have any question here then let me continue with the temperature scales there are three main temperature scales one is celsius or centigrade the other one is fahrenheit the other one is calvin okay in turkey celsius or centigrade is widely used and calvin is also widely used for scientific purposes okay so centigrade and calvin are very important temperatures case it is very easy to understand you already know from high school years so what is the celsius or centigrade temperature scale on this temperature scale 0 degrees celsius is the freezing point of pure water and 100 degrees celsius is its boiling point okay but in case of fahrenheit temperature scale 32 degree fahrenheit is the freezing point of pure water and 212 degree fahrenheit is its boiling point so what is the difference between 0 and 100 degrees celsius here in case of celsius temperature scale delta t is 100 degrees celsius okay between the freezing and boiling point of water but in case of fahrenheit the delta t between freezing and boiling point of water is 180 degree fahrenheit okay so you must be very careful and you can convert the temperature scale from celsius to fahrenheit by using this formula this is the fahrenheit temperature this is the celsius temperature you have to multiply celsius temperature with 9 and divide by 5 and you have to add 32 degrees then you can find the fahrenheit temperature and in order to convert from fahrenheit to celsius then you have to do this one this is five over nine times fahrenheit temperature minus 32 degrees do you have any question here related to the fahrenheit and celsius temperatures case then let me continue with the kelvin scale or absolute zero okay this gives us information about kelvin scale here you see a constant volume gas thermometer here we have a spherical shape it has certain constant volume made from metal okay and it contains a gas okay and its volume does not change volume is constant and you increase the temperature of this gas within this volume okay so then what will happen the pressure measured here in the pressure gauge will increase if you increase the temperature okay if you increase the temperature of this gas within this constant volume then the pressure of the gas will increase and you will see the certain pressure here this is the pressure gauge and on the right side i have a graph so what happens to the pressure here i have a temperature scale in centigrade or cells use and this is the pressure scale okay so here i have different types of gas let's say this is guess one and i increase the temperature from zero degrees celsius to the 200 degree celsius what do you see pressure increases within this constant volume the gas pressure increases and here we have another type of gas here we have another type of gas and they have also the same relation if you increase the temperature pressure of the gas increases if you increase the temperature pressure of the gas increases but if you decrease the temperature what will happen just consider that here you are using a cooling source okay then you cool down the gas okay so what will happen to the pressure if you cool the gas then pressure will decrease decrease decrease decrease and finally here at this point gas pressure will go to zero zero gas pressure and also for this gas if you decrease the temperature decrease decrease pressure decreases and finally when you reach to the minus 273.15 degree celsius the gas pressure within this container will be zero okay so this temperature is called as absolute zero okay because here gas pressure is zero and in the kelvin scale this temperature is zero kelvin okay here we have two scales this is the centigrade or celsius scale and here we have kelvin scale and we have gas pressure within this container we send this constant volume as a function of temperature and at 0 kelvin at zero kelvin we have zero pressure zero gas pressure within this constant volume okay and we have this relation between temperature and pressure if you increase the temperature you increase the pressure if you decrease the temperature you decrease the pressure so this is the kelvin scale and you can also convert the temperature from kelvin to celsius or you can convert temperature from celsius to the kelvin okay do you have any question here then let me continue with the conversion and here we have this information actually we have discussed this one on the kelvin or absolute temperature scale zero kelvin is the extrapolated temperature at which a gas would exert no pressure here we have discussed at zero kelvin the pressure of the gas is zero so in order to convert from celsius to kelvin you can use this formula okay this is the temperature in celsius scale plus 273.52 then you can find the temperature in kelvin scale here there is important information let's consider that here we have ice and water in this figure okay there are ice cubes many ice cubes and there is water and here you see a glass thermometer and you measure the temperature of this system let's consider that the temperature of this system is 0 degrees celsius and you would like to convert this temperature to the kelvin what is in kelvin okay so you can use this conversion here but you must be very careful there is no degree symbol here okay you should use just capital k okay so here there is a degree symbol and this is wrong representation don't use degrees okay in kelvin scale in fahrenheit scale we have degree symbol here you see in celsius scale we have degree symbol here but in kelvin scale we don't have any degree symbol don't use degree symbol in kelvin scale okay now let me show you relationships among kelvin celsius and fahrenheit temperatures case here we have calvin scale on the left side on the right we have fahrenheit scale and here we have celsius scale in between so we know that water boils at 100 degrees celsius and in kelvin scale it is 373 calvin and in fahrenheit scale it is 212 degree fahrenheit and we know that water freezes at 0 degrees celsius and in kelvin scale it is 273 kelvin in fahrenheit scale it is 32 degree fahrenheit so fahrenheit is used in real life or not yes it is used okay in some countries fahrenheit is used in turkey we use celsius scale and as i told you calvin is also used in industry and science very important temperatures case in in scientific researches and here we have carbon dioxide it solidifies at minus 78 degrees celsius okay and in kelvin it is 195 kelvin in fahrenheit it has different temperature what do you see here look at this temperatures case don't forget that kelvin scale is never negative okay the lowest temperature in calvin scale is zero okay but in celsius scale or fahrenheit scale we have also negative numbers below the zero okay don't forget this one and absolute zero is this one absolute zero is minus 273 degrees what was the meaning of absolute zero gases have no pressure zero pressure at this temperature and this is zero kelvin and it is minus 460 degree fahrenheit so let me also show you some applications and some different materials with different boiling temperatures here on the left side you see liquid helium actually helium is present as a gas okay in air but when you liquefy the helium it will have this temperature 4.2 kelvin it is very close to the absolute zero okay so you see that in status use it is minus 269 degrees celsius it is very low temperature okay for this reason liquid helium is very cold and there is a liquid nitrogen here it has boiling point 77 kelvin okay so below this temperature nitrogen nitrogen is present in the air okay and this nitrogen liquefies below this temperature 77 kelvin okay it is also very cold liquid and in celsius it has temperature of minus 195 degrees celsius very low temperature and they are very important liquids for health applications for industrial applications for example you would like to store the vaccines you would like to store the medicines okay then you would like to store some cells for scientific purposes you can use liquid nitrogen and liquid helium is also very important for example in magnetic resonance imaging in the hospitals there are mr machines okay in order to take the two-dimensional pictures of the bodies and within this systems there are huge superconducting magnets and this superconducting magnets are cooled by using liquid helium so these two liquids are very important for our daily life and they are also widely used in daily applications in industry and also science and how to deal with this very low temperatures i'm talking about 4.2 kelvin actually they are very dangerous liquids okay because they are very cold and you must be very careful when dealing with this very cold liquids here for example on the right side there is a diver or tank which contains liquid helium and the temperature of this liquid helium is 4.2 kelvin or minus 269 degrees celsius okay very low temperature and if you are dealing with this temperatures you must be very careful you have to use special gloves okay these are made from family insulating materials and you must be very careful and in addition to that just look at this tank here within this tank on the right side we have liquid helium and this is the temperature but we have temperature of overall temperature of the room is 300 kelvin or let's say around 27 degrees celsius okay but here within this tank temperature is 4.2 kelvin so in order to insulate the air and the liquid helium within this tank you have to produce special tanks and this tanks have also thermally insulating systems like this actually within this type of d-words there is a insulating okay here outside the temperature is 300 kelvin or 27 degrees celsius let's say and here we have liquid helium and temperature is 4.2 kelvin okay so this thermally insulating material can prevent very fast heating of this liquid helium so what is used usually liquid nitrogen used here or vacuum is used okay what is the meaning of vacuum you have very less particles then you can also consider that vacuum is thermal insulator okay so you can use liquid nitrogen here or you can use vacuum then you insulate this liquid helium from the environmental conditions then you can keep this liquid helium cold for a long time and this tanks must be very powerful against the thermal expansion if you heat the liquid helium here there will be gas helium and if you further heat the liquid helium then you will have huge gas production in a very short time and this gas will expand and expand then it may explode okay so then you have to use very powerful materials against this huge gas increase within this helium tanks or nitrogen tanks in addition to that there are safety valves here okay and you release the increased pressure by using the safety valves so when you are using liquid helium or liquid nitrogen you must be very careful and you should available safety issues do you have any question here this is the bio application mammalian body temperatures from the book most mammals maintain body temperatures in the range from 36 degrees celsius like humans to 40 degrees celsius a high metabolic rate warms the animal from the sun and insulation such as fur and body fat slows heat loss let's consider this animals are living in winter and let's say outside temperature is 30 degrees celsius okay and this is the body of this animals and they have body temperature of let's say 38 degrees celsius okay and here we have very low temperature here we have let's say relatively high temperature how to save this temperature within this body you need a thermal insulator what is this thermal insulator fur or body fat provides this tamil insulating okay and look at this space application this is the international space station and there are astronauts here and they live there they study there they are doing research now within this international space station and what about the temperature in space the baseline temperature of outer space is around 2.7 kelvin we are talking about minus 270 degrees celsius okay so how to provide living conditions within this one okay you need thermal insulation and look at the astronaut here he or she repairing something in international space station okay and the outside temperature is around roughly 2.7 kelvin okay very low temperature and you need thermal insulating materials or when space shuttles enter into the atmosphere of the world their temperature rises up to very high temperatures okay and you have to use very good timely insulating materials okay and also in industrial applications these things are very important do you have any question okay let me continue with thermal expansion what is tamil expansion if you increase the temperature of material then its volume expands its volume increases okay and if you decrease the temperature then its volume shrinks thermal expansion tamil shrinking they are very important in industry in engineering and here on the right side i have already mentioned you see a gas thermometer there is a container and it contains a gas if you heat this gas if you increase the temperature of this gas then the gas within this material expands okay and then pressure increases okay and here we have bimetallic strip we have two metals and if you heat these metals then they will expand okay so this is the tamil expansion and we have also many examples in our real life for example if you have a completely filled and tightly cat bottle of water that's considered this part is tightly kept and then you have water within this bottle and if you heat this water then the material will expand expand expand and finally you can crack this bottle or as i told you in case of helium or nitrogen diverse okay there are release wires so you can decrease the pressure of the cinder diver but if you don't have any wealth here and if they are closed and helium vaporizes and the pressure increases increases increases and this tank can explode like a bomb okay so the pressure can crack this dewar and you can use this thermal expansion property to loosen a metal jar lid by running hot water over it so let's consider that this white lid is very tight and you cannot open it and if you drop hot water okay on this metals then they will expand and you can easily open them so there are many applications but you must be very careful with tamil expansion in our real life in industry for example you are designing or producing an engine in industry okay and the temperature in the engine changes by time so let's consider in gene in ships in gene in submarines in gene in planes okay or in gene in missiles or engine in motors in in cars so you use metals and thermal expansion of this metals are very important because temperature of the engine changes a lot okay at the beginning it is let's say cold at room temperature and then it reaches up to very high temperatures and thermal expansion becomes very important for engineering applications and let me continue with the linear tamil expansion so if you increase the temperature of a rod then its length will increase it will be expended okay so how to define this change in length it is given with this equation here this is delta l the change in the length of the rod and this is the alpha coefficient of linear expansion and it is specific for each material okay each material has certain coefficient of linear expansion here we have l0 this is the original length and this is the delta t change in the temperature so you change the temperature of the rod then you change its length here we have example there is a rod here and the length of this rod at the beginning is l0 this is the initial length and temperature is t0 okay let's consider 300 kelvin room temperature okay and you heat this rod and you increase the temperature now the temperature is higher than the room temperature and we have here delta l there is an expansion and this delta l is given with this one so if you increase the temperature then the length will increase it's vice versa if you decrease the temperature then the length will decrease so if you increase the temperature with two delta t then the length will increase with two delta l because this delta l on the left side of the equation is directly proportional to the delta t okay and what about the initial length here here you see initial length l0 this one okay so we have here a road it has certain l0 initial length and temperature is t0 and i increase the temperature then it is expanded this is the new length of the rod and here we have rod from the same material but now length is two times bigger than the initial one and temperature is again the same and i increase the temperature with the same amount here which i have increased what do you see here the increase in the length is given this 2 delta l compared to this one because delta l is given with alpha l zero delta t it is directly proportional to the initial end if you have two l0 here then here you will have 2 delta l this is the linear tamil expansion so due to the temperature increase material expense if you decrease the temperature of the material then temperature can shrink and what about the molecular basis of thermal expansion here you can consider that there is a crystal and these are the atoms on the corners okay and let's consider that these atoms are connected by springs okay actually this is not the case but this is just representation and this is the average distance between the atoms this one okay when the temperature increases the average distance between atoms also increases okay and this this one atoms get farther apart and every dimension changes just look at this one here just consider we have a material with this shape and within this material we have millions of atoms and between atoms we have this certain distance okay if you increase the temperature okay then this average distance between atoms increases and then material expands now this is the neat dimension of the material after heating okay because temperature changed okay this is the explanation in molecular basis so what happens to the average distance between atoms this is the potential energy of the two atom system let's say and this is the distance between the atoms and during the last lecture we have seen that the potential energy between two atoms is given with this relation and here we have an average distance equilibrium distance okay so here at this condition we have minimum energy okay minimum energy and atoms are happy to stay at this condition with some certain average distance between them so if you increase the temperature you increase the energy of the system okay then we have never energy then this is the average distance between the atoms here in equilibrium we have this average distance x is this one x equilibrium let's say x1 and if you increase the energy of this system if you increase the temperature of the system then average distance will be like this and if you further increase the temperature of the system average distance will be like this if you further increase the temperature of the system if you further increase the energy then this is the average distance between the atoms so what will happen this average distance will increase okay then in total material will expand this is the explanation of tamil expansion in molecular basis and what about the expansion of holes and volume expansion it is very important here we have a cold material or let's say the temperature is around room temperature 300 kelvin or let's say 27 degrees celsius and you heat this material and now it is hot okay so the new temperature let's say 400 kelvin okay or you can also convert into the degree celsius and now we have bigger volume okay material is expended right but what happens if we have a hole within this material the hole within this material will also expand okay don't forget this one this is very important sometimes students think that this hole will be smaller after tamil expansion but this is not correct the hole will also expand okay now we will have bigger hole within the material after tamil expansion because just consider that here we have atoms okay and after heating the average distance between atoms increases okay so this is the new situation after camel expansion and here we have atoms they have certain average distance in equilibrium condition and after tamil expansion the average distance between the atoms is increased okay you can consider like this and what about the volume expansion this is the equation for the linear expansion and delta l changes by temperature okay this is the linear thermal expansion and what about the volume tamil expansion it is given this delta v change in volume it is equal to beta coefficient of volume expansion this is v0 original volume initial volume and this is the delta t change in the temperature or temperature change this is the volume expansion and here we have coefficient of linear expansion it is very important table for technological industrial applications and also for daily life so each material has certain unique alpha okay so you change the temperature of the aluminum for example let's say you change its temperature 100 kelvin or 100 degrees celsius then its length will increase but with the same change in the temperature of the glass let's say again delta t is 100 kelvin so you have same delta t you have same l0 but you will have different delta l you will have different linear expansion because glass has much lower linear expansion coefficient compared to the aluminum or brass okay so you provide same delta t you increase the temperature in same amount but the expansion is different because linear expansion coefficient is different and here we have quartz fused quartz so it has very low thermal expansion and for technological applications look at this one for military applications for technological applications this information is very important okay so very low tamil expansion coefficient is required for some applications so here there is another special material the name is invar it comes from the in variable in variable dash mass okay this is the spatial nickel iron alloy and it has very low linear expansion coefficient compared to the aluminum compared to the copper compared to the pure nickel compared to the pure iron it has different thermal expansion coefficient and very useful material for industrial applications okay so for industrial applications you need very low thermal expansion coefficient material otherwise when the temperature of the material changes then its shape will change and it is very bad for some applications just consider satellites okay just consider that this is the earth and here there is a satellite these are the panels solar cell panels let's say okay and within the satellite just consider you have a camera just consider you have sensors okay and other electronics what is the temperature in space baseline temperature is around 2.7 kelvin let's say okay and there is also sun and the radiation comes from the sun can increase the temperature of this satellite up to let's say 400 kelvin okay then what do you see here every part within this satellite in space the parts in the camera departs in the sensors and those electronics part have this temperature change many times per day okay so they are cooled and they are heated they are cooled they are heated so with this temperature change the camera shouldn't be affected sensors shouldn't be affected electronics shouldn't be affected okay so it is very important to use low linear expansion coefficient material in this type of applications okay i will not go into detail but for real life this information is very important and here we have again coefficients of volume expansion again here you see beta value of this was volume expansion beta initial volume and change in the temperature okay so if you have low beta then you will have low thermal expansion in the volume so we have brass we have copper these are the metals they have more the same volume expansion coefficient here we have glass relatively low here we have invar again iron nickel alloy which i have discussed here very important technological material here we have a quartz even lower okay and here we have steel it is also metal okay so you see different coefficients of volume expansion and let's discuss some examples of thermal expansion this is the railroad track and this is the metal okay if you use high thermal expansion material here then the road will be destroyed during hot days and during cold days the volume shrinking will occur okay so then you can destroy the railroad this is very important and you have to use special special materials special steels special alloys for these applications if there is huge tamil changes in the system so what you see here there is a gap okay and this gap is used against tamil expansion so on hot days the segments expand and fill in the gap if there were no gaps the track could buckle under very hot conditions and look at the bridges maybe you always see these gaps in the bridges there is a huge gap and during the hot days this gap will decrease and cold days this gap will increase okay if you don't put these gaps on bridges then they can collapse so look at this part of joints in buildings okay there is a gap here between two parts of the building in hospitals in university buildings in shopping centers i mean in big buildings you always see these joints and this joins these parts against tamil expansion okay if you don't use this joints then the building can collapse so this is the example of tamil expansion and let's discuss the tamil expansion of water so what we have discussed up to now that if you heat a material if you increase the temperature of the material then material will expand if you cool down the material then material will shrink but water is exception what happens in water between zero degrees celsius and 4 degrees celsius water decreases in volume with increasing temperature so here on the top picture you see water volume versus temperature this is the zero degree celsius this is 100 degrees celsius and what do you see here that the water volume increases this temperature water expense as temperature increases but at this low temperatures here in this region water has different behavior this is the volume this is the temperature and between zero degrees celsius and four degrees celsius what happens you increase the temperature okay delta t is increased it is positive but volume decreases what do you see here delta v beta v zero delta t you increase the delta t then you should increase the delta v but between zero and four degrees it works vice versa okay in water because water is an exceptional case for this thermal expansion okay and this property of the water is very important for the life in lakes okay with this property because of this anomalous behavior lakes freeze from the top down instead of from the bottom up so this is the exceptional case in tamil expansion and let me continue with the tamil stress what is tamil stress here you see again a bridge this is one part of the bridge road this is another part of the bridge road and here we have a gap okay and during the hot days this gap will decrease during during the cold days this gap will decrease okay and if you don't use this gap just consider that you are building road like this and there is no gap here due to the thermal expansion due to the tamil expansion during the hot days they will apply force each other and then this bridge can be broken can collapse okay for this reason we use expansion joints in civil engineering expansion joints on bridges are needed to accommodate changes in land that result from thermal expansion and what about this thermal stress applied on the neighboring part of the road due to the temperature change which is given with this one this is the thermal stress force needed to keep land of road constant and this is the cross-sectional area of road this is the young's modulus which we have discussed in previous lectures this is the coefficient of linear expansion and this is the temperature change so if you increase the temperature then we have a thermal stress okay we have a thermal stress and you have to use expansion joints on bridges on buildings against this time of stress so let me discuss an example here an aluminium cylinder 10 centimeter long with a cross-sectional area of 20 square centimeter here we have an aluminum rods okay initial length is 10 centimeter and the cross-sectional area is given 20 square centimeter it is used as a spacer between two steel walls and here we have a steel wall okay and here we have another steel wall at 17.2 degrees celsius it just slips between the walls so this aluminum can move easily okay at 17.2 degree celsius but what happens if you increase the temperature up to 22 degree 22.3 degrees celsius calculate the stress in the cylinder and the total force it exerts on each wall then then it warms to 22.3 degrees assuming that the walls are perfectly rigid and a constant distance apart so at this temperature 17.2 degrees celsius this aluminum rod can move and can move up and down easily and you increase the temperature to this value then what you make what you expect this road will expand so new land will be bigger than this previous land okay then you cannot move this aluminum rod anymore so what about the calculations if you know the thermal stress formula which we have seen in the previous transparency it is easy to calculate it this is the time of stress force per area young modulus of aluminum linear thermal expansion coefficient of aluminum and the change in the temperature so this is the final temperature this is the initial temperature 22.3 degree celsius minus 17.2 degrees celsius and the change in the temperature delta t is 5.1 degrees celsius or 5.1 kelvin okay then just put the young modulus of aluminum here 7 times 10 to 10 pascal and just put the linear expansion coefficient of aluminum here 2.4 times 10 to minus 5 1 over kelvin and just put here the delta t change in the temperature then the stress can be calculated as minus 8.6 times 10 to 6 pascal okay so what about the force the total force is the cross-sectional area times the stress so we have found the stress here okay we have calculated this stress and then it is given this force pair area and i have calculated stress and i know the cross-sectional area then i can calculate the force and force is this one minus 1.7 times 10 to 4 newton or minus 1.9 tons it is huge this small cylinder applies huge force okay if you change the temperature so when you are designing an equipment or an engine in industry in engineering okay you must be very careful so just consider aluminum engines used in cars okay so even very small change in temperature so five degrees celsius change in the temperature can produce huge thomas stress you must be very careful okay let me continue with the heat do you have any question until this part so let's discuss the quantity of heat sir james jewell in 19th century end of 19th century studied how water can be warmed by vigorous steering with a paddle wheel here we have a water within a bottle okay and here we have a paddle wheel you see there is a paddle wheel and this is connected to this one with the rope and drop is attached to this mess here and this mass goes down and it is rotated then paddle wheel within the water is also rotated very fast okay so the water warms as the paddle does work on it so what do you see here we have a weight which is given with mg right and let's say this is y is equal to zero ground and this is the y is equal to y one okay and what about the work work is given this force times displacement okay then force is given with this one displacement is this one and then we have a verb okay so the water warms as the paddle does work on it the temperature rise is proportional to the amount of work done if you put here a temperature source okay then you can also produce the change in the temperature so here we have a definition the calorie abbreviated cal is the amount of heat required to raise the temperature of one gram of water from 14.5 degrees celsius to the 15.5 degrees celsius so what about the change in the water temperature one degree celsius you have one gram water and you would like to change its temperature one degree celsius and it is called as one calorie okay this is the amount of heat required to raise the temperature of one gram water from 14.5 degrees celsius to 15.5 degrees celsius so now let me continue with the quantity of heat q so here we have heat required to change the temperature of a certain mass here we have water it has certain mass and i would like to change its temperature okay then i need heat okay so the quantity of heat q required to increase the temperature of a mass m of a certain material by delta t here i have a bottle of water and its mass is m and i would like to increase its temperature this delta t then i need heat to increase this temperature and this heat required to change the temperature is given with this equation you already know from high school years m times c times delta t this is the change in the temperature this c is specific heat of material and it is also unique for each material and this is mass of the material so for water for example the specific heat of water is approximately 4190 joule per kilogram per kelvin let me continue with this example 17.6 from the book overheating electronics this is very important for daily life you are designing an electronic circuit element made of 23 milligram of silicon mass is here silicon material which is used which is mostly used in electronic circuits the electric current through it at energy at the rate of 7.4 milliwatts or 7.4 times 10 to minus 3 joule per second if your design doesn't allow any heat transfer out of the element at what rate does its temperature increase the specific heat of silicon is given so just consider that here you have a silicon board and here you have conducting lines okay so you have live voltage between these two ends of the wire and then there is a certain current okay so due to this current this material will be hot okay and then if you don't use any cooling sources then this will damage your electronics for this reason electronics parts usually cool by using fans or by using other metal coolers okay this specific design so let me solve the question and then talk about its importance in electronics so what about the formula remember the formula q is given this m c delta t okay what is given here we at the energy at the rate of 7.4 milliwatt or 7.4 times 10 to -3 joule per second so we have this one to give the energy into the system it is given okay and this one is s what is the change in the temperature by time so if you divide this one with dt if you divide this one dt then you can write this expression so this is asked this is given in the question 7.4 times 10 to minus 3 joule per second mass is given 23 gram you have to convert this one into the kilogram then here we have specific heat of silicon c which is given in the question then this is the rate of change of temperature what do you see here the temperature changes by time is this relation 4.46 kelvin per second it means that 27 kelvin per minute or 27 degrees celsius per minute let's consider you have electronics okay and the temperature is 27 degrees celsius at the beginning and you drive current then so each one minute you increase temperature 27 degrees celsius so after one minute after one minute the temperature is 54 degrees celsius and after two minutes what is the temperature the new temperature of the system is 81 degrees celsius so you can destroy the electronics okay this is huge temperature within two minutes the temperature increases up to 80 degrees celsius and very dangerous for the electronics and usually in electronics coolers are used okay if you open your computers you will see this type of coolers on the motherboard or in other electronics and usually special design used in electronics for example what do you see here we have many circuit elements capacitors resistors and what else inductors so we have many circuit elements here and in addition to that here we have an aluminum block what is the duty of this one this is the cooler okay this is a metal cooler so it has many surfaces so via this surfaces in it interacts with the air and then cools down the temperature of the circuit board and this type of coolers you can see more or less in every circuit element let's talk about the molar heat capacity the quantity of heat required to increase the temperature of n moles of a certain material by delta t so i have a material and it has molar heat capacity c and i would like to increase its temperature okay and this is the number of moles of material this n here so the quantity of heat required to change the temperature of a certain number of moles is given with this expression for example here we have molar heat capacity of water it is approximately equal to 75.4 joule per mole per kelvin so what do you see here we have a table for specific heats and molar heat capacities on the left column here we have specific heat c and here on the right column we have molar heat capacity capital c okay so again you see that each material has different specific hits and specific molar heat capacities here we have aluminium beryllium copper and what do you see here is ethanol and ethylene glycol have very huge specific heat and also very huge molar heat capacities compared to the other materials and here we have water for example liquid it is around 75. look at the aluminum compare the aluminum and water water has three times bigger more is molar heat capacity compared to the aluminum okay look at the iron so it is also around 26 and what else here we have lead and here we have copper metals usually have more or less the same magnitude of molar heat capacity let's say and here we have water which is quite different we have marble here quite different and here we have ethanol which has quite different molar heat capacity and in applications these properties are very important in industrial applications and here i have last transparency here we have a glass and we have water within the glass and you would like to change temperature of this water within this glass so then we have this relation i would like to increase the temperature of the water and how much heat is required to check to produce this change in the temperature of water water has a much higher specific heat than the glass or metals i have discussed here this is the water and these are the metals and water has more or less three times bigger molar heat capacity compared to the metals and used to make cookware for example in kitchen usually we use glass materials or metal materials to make cookware right so and then this ex helps explain why it takes several minutes to boil water on a stove even though the pot or cattle reaches a high temperature very quickly so you can change the temperature of metal objects quickly why look at the formula let's consider you would like to produce temperature change 100 degrees celsius of aluminium pot let's say this is aluminium pot and you would like to increase its temperature with 100 degrees celsius and what about the molar heat capacity of aluminum it is around 25 let's say okay here where is it aluminum 24.6 molar heat capacity and this is the heat required to produce this change so this aluminum has 25 just consider water and here within the aluminium pot you have water and water has around 75 molar heat capacity and you would like to produce same temperature change 100 degrees celsius this is delta t this is c of water and let's say same end number and what about the q for the water you need much higher to compare to the aluminum okay so you need more heat for this reason it takes several minutes to boil water on a stove even though the pot or cattle reaches a high temperature very quickly so you can produce this huge temperature change in aluminum or glass okay but in water it requires more heat so this this one i finished my lecture take care of yourself bye