okay and so we know how to in general right uh from an engineering standpoint we haven't built anything here right but we have sort of a general understanding of heat pumps oh i should have talked about the heat pump sorry can i go back to that so in a heat pump it's ever so slightly different from a refrigerator because in a heat pump what you're trying to do and i'll just use the home heat pump as an example you put pipes down into the ground water and you take energy out of the groundwater and make it colder now it's it's an interesting phenomena almost everywhere if you dig down in the ground about five six feet the temperature is about 50 degrees anywhere okay it varies a little bit it depends winter and summer but but when you get that far down it's almost always about the same okay so a heat pump says hey i'm going to take energy out of that 50 degree water to heat the house well this seems counterintuitive right how can 50 degree water make my house be 68 well it's because i can take that 50 degree water and take energy out of it and make it 49.9 because there's a lot of water there right make that fractionally kohler take that energy and use that energy to put it into the gas make the gas warmer make the gas hot now so that now when the hot gas comes in contact with the air in the room it adds that energy into the room air okay uh they are very much more efficient than burning fossil fuel okay they don't work you can also do it with air this is basically what your air conditioner does right you you move energy i'm going to go back to the heat pump you can have an air heat pump where you say i'm going to take a i'm going to take energy out of the outside air and move it through my gas cycle and have warmer air in the house you're going to take energy out of the air in michigan this is a bad idea because what's a typical air temperature in the winter time really cold and you're going to try to take energy out of something that already doesn't have much right and put it into the house what so groundwater works better but if you want to do a groundwater heat pump you have to dig wells down into the ground and things like that right so they're expensive to install efficient to run okay but in florida heat pumps are great you can use them to do air conditioning in the summer and heating in the winter and they're efficient and life is good in michigan not so much so we burn natural gas okay yeah that they're very efficient but they don't make a lot of heat right and when you have a cold winter morning and you're don't put your socks on yet you want warm air in the house right and you want it to warm up really quickly when you say hey i'm going to turn the thermostat up so you don't see them too much in michigan but but they are they are a good thing mr smith we want a good efficiency right we don't want to we don't want to pay lots of dollars either for our hot energy if we're doing an engine we don't want to pay lots of dollars to the electric company to move a little bit of energy if we're trying to do air conditioning yeah so and now it's an engineering question because remember i said you can put any cycle you want at the heart of either the heat engine or the heat heat pump okay uh a an engineer slash physicist named carnot worked out that the most efficient system you can ever do is the carnot cycle it's two isotherms and two adiabatics okay it ain't nothing better right it's a it's a involved proof to convince you that there isn't anything better but this is it okay this cycle is the most efficient okay now your car which is your heat which is your most common heat pump does not run on the car no cycle it runs on the auto cycle but if this is the most efficient why don't we use this one it does not okay if this is this is very exaggerated okay this picture but the air the purple area in a car no cycle is really tiny it's the most efficiency but the amount of work you get out of one cycle in a car no engine not much so if you tried to make your car out of a carnot cycle i mean i got a little wimpy thing out there it's like 90 horsepower okay no maybe no fraction of horsepower okay um we have little cardinal demonstration engines i didn't get it out because i didn't want to start a fire but they're at the level of you have a little fan blade that you can make spin with the car and it kind of it goes around like this but it is efficient okay uh now how efficient is it well here we get more formulas for your formula sheet so here we go greg okay the efficiency of a carnot engine which is the best you can do is one minus the temperature of the hot side divide the cold side divided by the temperature of the hot side so if we think about trying to do this in an automobile right the hot side i don't know uh five six seven hundred degrees kelvin maybe right for the hot part of that and and the cold part maybe like 300 kelvin for what comes out of the tailpipe okay so if we had 600 and 300 that'd be like uh that's a factor that's a uh that's a half our efficiency would be fifty percent before we had any frictional losses before we had anything else best we could do sixty percent okay sorry 50 uh the power plant over there okay uh maybe gets up to 60. palisades nuclear comes in around 35 percent okay it that's depressing isn't it if you think about you know as we run out of energy because oil reserves are depleted and we mined all the coal and all that every time you i mean we're just throwing dollar bills out the window all the time okay because inherently the second law of thermodynamics says you can't win none of that you will lose you can't even break even on this now i could improve my uh efficiency in two ways i could make the cold side colder that would take that bottom blue line there move it down right which would make the purple area bigger yeah okay uh yeah uh how do you do how do you do that how do you make the cold side colder well you got to have a cold reservoir right lake macatawa lake michigan gulf of mexico i mean what's the temperature range for these right maybe they range from you know 30 degrees c to 20 degrees c we're sort of stuck with this average temperature on the surface of the earth that's hard to beat well well we'll use liquid nitrogen for the cold side yeah that's going to be efficient right because you're going to need enough liquid nitrogen that as you add energy to it you don't change the temperature okay that's not going to happen okay you could also imagine getting higher efficiency charles if i make the top one go up okay if i if i run my car no engine with a hotter hot side okay the problem with this is and autumn auto manufacturers are actively looking into this but the biggest reason why it's hard to move the hot side up in your automobile you don't want the engine to melt right and that puts a constraint on it because if we go to the chemistry tables and we look at the melting points of metals well yeah right some of them melt at higher temperatures than others like aluminum has a fairly high melting point and in the 60s and 70s automakers actually made car engines out of aluminum okay the the difficulty was that frictional wear and aluminum uh aluminum is relatively soft and so after 50 000 miles they were burning oil because the inside was just all worn out from friction and people got really mad okay if you make the temperature hotter in the formula well if if you divide by a bigger hot then that gets smaller so one minus something smaller is bigger right and one would be perfect but one's not going to happen because the only way to get one would be to have the cold side be at absolute zero yeah that's going to be practical for a car the automakers many some of the automakers are looking into ceramic engines because ceramics have higher melting temperatures maybe maybe not who knows well most power plants don't exhaust their air to don't exhaust their heat to the air they exhaust it to the water yeah but it's it's what it's the difference between 300 and or like 27 293 and 295. so yeah probably marginally but not hugely the the biggest way power plants get their efficiency is they um make the steam hotter and that's why nuclear power plants are slightly less efficient than natural gas power plants because you can burn natural gas and get the steam hotter oh because if you make the steam hotter you've raised the hot side it's easier to get efficiency by making the hot side hotter than it is by making the cold side colder no no the steam is the is the complicated fluid that goes around so uh we're going to take a little detour here real quick right in a power plant you have something that makes makes hot like burning natural gas the fluid is a steam water mixture so it's complicated because their phase change is in there too but you heat the steam the steam goes into the turbine the steam is expanded it's under high pressure it does work against the turbine to spin it and turns into water but the water is still fairly warm so you got to get the energy out of the water so that it can go back and pick up the energy and turn back into steam okay so it gets i mean we're not going to do these complicated ones in here your refrigerator as well is much more complicated than what we showed there because it involves two phase changes where it turns liquid to vapor and vapor back to liquid okay but the general ideas still hold in here if you want to make it more efficient it's got to run hotter okay in now you notice little c on the efficiency there hope you see the little c that that formula works for carnot okay if you if you have any cycle be it carnot or be it the otto cycle or the hope cycle or right whatever okay you can always find the efficiency by looking at the amount of heat and if you think about this if if we look at that formula q hot minus q cold that's the work that's what you want right you want more work divided by what you had to pay for which is the hot cue so it's a good measure of efficiency right it's what you got divided by what you paid for yeah the the first one the left one works for any heat engine the right one is only applicable to a carnot engine okay uh now the industry got a hold of the heat pump right and they they define and i didn't even write them all down there are other measures of how good it is but in general for a heat pump we worry about q hot over work well yeah samantha right because in my heat pump i want q hot that's what's going into the room to make me comfortable i paid for it by paying for w so it makes sense that coefficient of performance for a heat pump i'd like that number to be big as possible right but that's because i want useful heat and i'm buying the work it's interesting here though if you look at the diagram right the the work that normally you think might get wasted or whatever right actually works to warm the house as well so it's not only the energy you take out of the ground it's also the work that's being done on it that ends up being available to warm your house okay if you have a refrigerator ben okay now you're trying to maximize the q cold relative to what you paid for because you don't care about whether your refrigerator makes your kitchen warm or cold you care about making the food cold right and do you get the shift in the heat pump you're really trying to work on the on the hot side right this minute you're trying to make your room warmer by putting energy into the room in the refrigerator you're not worried about whether you make the kitchen room you're worried about making the food cold right so when we characterize the performance of a refrigerator we say oh how much energy did i take out of the food and what did it cost me well it cost me the work so you get two different definitions for for how well your physical device is working now most people these days when they go to home depot to buy a new refrigerator all they do is look at the stars is it five star four star three star juice right if you look on the yellow sticker you can find these numbers nope nobody looks i doubt it uh because the the bigger the temperature difference in your engine the more efficient the bigger the temperature difference in your refrigerator the less efficient okay so it's harder to refrigerate things than it is just to cool them okay uh oh i already said it but don't put a refrigerator in the garage because you never get the heat out of the gas and it doesn't work and then of course addison last one you thought you were going to miss it didn't you you were hoping uh all these devices have friction okay so our nice theoretical picture well if we're doing our heat engine on the right hey the friction just goes and we don't reckon we don't realize it is work it it turns out it just goes it we just waste it okay that portion of the work that you might have been able to have from thermodynamics based on the second law no you never quite get what you expected because the friction just heats up the air right you drive your car long enough you get out you put your hand on the tires they're warm right because of frictional losses if you watch nascar they have blowers on the brakes and the bearings and all that stuff because they get hot in addition to the ideal thermodynamics and the same thing your refrigerator well yeah there's a certain amount and the energy goes back into the food why we don't want that right but it's just the reality of life okay so you make it cold but some of it just lowers the efficiency even more okay uh it is amazing how inefficient the things in your life really are okay we waste so much energy uh just by turning things on okay questions you made and i heard you tell greg there's a moodle assignment for is it friday saturday it's short but it might get longer so keep checking or there might be a a b version okay hi i have questions i agree