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prove that Cp - Cv =R

Please refer the following link:
https://www.meritnation.com/ask-answer/question/define-the-two-principles-specific-heat-of-a-gas-and-derive/thermal-properties-of-matter/1564342

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here,

Cv - molar specific heat at constant volume

Cp - molar specific heat at constant pressure

where, according to the first law of thermodynamics,

Cp = (1/n)(dU/dT) + R

or for ideal monoatomic gases

Cp = (5/2)R

and

Cv = (1/n)(dU/dT)

or Cv = (3/2)R

thus Cp - Cv = (5/2)R - (3/2)R

or

Cp - Cv = R
hope it helps!!

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HEAT CAPACITY AT CONSTANT PRESSURE=Cp AND HEAT CAPACITY AT CONSTANT VOLUME IS Cv
AT CONSTANT VOLUME THE EQUATION OF HEAT IS
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