define the two principles specific heat of a gas and derive the formula to show that Cp- Cv=R

Hello!

Molar Specific Heat is defined as the the ratio of the amount of heat required to raise the temperature of 1 mole of a compound 1oC.

Now,

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

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