What is temperature

Temperature is property of any matter which tells the sensitivity of hotness that we will feel when we touch it.How ever it does not signify how much total energy it contains.For example of same mass of water and coal at same temperature coal has absorbed more heat because its heat capacity is higher.But since temperature is aproperty which is associated with average of its molecules of the substance is having you feel the same sensitivity when either coal or water at same temperature is touched with bare hands.
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From maxwell distribution we see that as temperature increases the the curve tends to be more flat that means average energy of molecules increases with rise in temperature.

It is different from entropy(a measure of randomness of molecules).For example if water and coal are at same temperature and have same mass and same amount of heat is supplied to both,coal will undergo more entropy change and less temperature change ie energy distribution among their molecule will be more random and average energy per molecule will be less compared to water. That means energy distribution among its molecules will be less uniform.So if heat is given to a substance and its temperature does not rises and substance does not do any work then it entropy increases which means the whole energy given is not distributed uniformly among its molecules which indicates the molecules are in random movement so transfer of energy among its molecules do not take place very often and therefore most of the energy is concentrated among few number of molecules.

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