Why is heat capacity not constant over large temperature arnge?
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The behavior of gas when heat is supplied, the pressure and volume change in temperature and the amount of heat required to raise the temperature for 1gm of gas through 1°C depends on the way gas is heated. You can use several sets of values of P and V heat the gas.
Therefore, specific heat possesses infinite values. The specific heat of the gas is not constant if you do not supply a constant amount of heat. So, you must have specific heat at a constant volume or pressure.
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