in this video i'll talk about how does the density changes with the temperature the first thing you need to understand what is the density mean the density means the how much mass you have in a unit the volume so if you take a different substances different materials the exactly the same volume then the mass would be the different so the density is defined is in unit volume how much you mass you have the more the mass in a unit volume is the higher the density is and that's how we define the density in order to compare one material or one substance to another substance so the density is denoted by rho and defined as mass per unit volume now let's say you have a liquid which is filled in a beaker or in any bottle or something this is the initial volume i v i stands for the initial volume the rho y is the density at that particular temperature which is t i and is the mass once you hit this material or when this liquid then we call the volume changes and the volume is vf that's the final the volume the density also changes and we call the density to be rho f this is pronounced as rho r o r o h o r h o row and this this is the notation for the density the mass does not change if you have the mass it doesn't matter where you take it you take it to the moon you take it to the jupiter you take it to the saturn the mass does not change or because even the temperature changes the only parameter that changes in the volume and the density the mass always remains constant and tf is the final temperature so with the increase or with the change in the temperature the volume changes the volume expands and the change in the volume is given by this formula here and again how does this coming from you need to understand the volume coefficient of the material and the link for the volume expansion coefficient is given below so the delta v is the initial volume the beta this is beta here is the volume expansion coefficient what we call the coefficient of volume expansion and delta t is the change in the temperature what is this delta v again means the delta v means the change in the temperature which is the final temperature minus initial temperature that's how we call the change in temperature so i'm simply writing vf minus vi and this term is exactly the same term here so i'm solving for vf so the vf will be if i take to the other side and take vi out it will be 1 plus beta delta t so the density at this temperature at the final temperature how do you define the density at this temperature again how much mass you have and what's the volume so get the mass for unity volume and this volume is at the final temperature the mass as it is because mass does not change and the volume is now given by this equation v i times 1 plus beta delta t this is exactly the value i plugged in here okay so the mass per unit vi is now the density at the initial temperature that i call rho i and this term is exactly as it is so this is now an equation or an expression for calculating the density with a change in the temperature and what you have to notice here it only depends on one parameter that's that is the beta which is the coefficient of volume expansion for most materials if you look at the most materials the density decreases with the increase in temperature because for most materials the beta is positive it's greater than zero but not for all materials there are certain materials or there are materials whose beta or the coefficient of volume expansion is negative within a certain temperature within a temperature regime it is negative and the water is the one interesting example if you look at the water the water has such a peculiar the coefficient of volume expansion and between zero degrees to four degrees celsius the coefficient of volume expansion for the water is negative and that is that has played such a vital role on the survival of many animals inside the lake inside the pond inside the ocean and and this is due to due to this region the water has the greatest density at the four degrees celsius let me explain one day for water between zero degree to four degrees celsius if we increase the temperature the beta the beta is negative that means the density the density increases if we increase from go from zero to four degrees celsius the density increases and the maximum density of water is at 4 degree celsius so even if the lake is frozen entirely frozen at the bottom it has to be the liquid water because the liquid water has the greatest density or occupies the maximum density and the densest material always sinks at the bottom so with this example you might have understand understood now even the lake is frozen where do the fish or the animals survive inside the frozen lake because in steep inside the frozen lake there is the liquid water and that might be the 4 degree celsius so remember this formula to calculate how does the density changes with the the temperature this is it from this lecture again if you have any questions 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