Question

Prove that CP - CV =R for one more of an ideal gas?

Answer 1

We know dQ =dU +dW

for 1 mole we take n=1

now, nCpdT=nCvdT+nRdT

or, n (Cp_Cv)=R

as n=1, then Cp_Cv=R (proved )

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Answer 2

Due to Mayer's formula,

∆U = ∆ Q + ∆ W

At constant pressure,

( ∆U = Cv∆T)

( ∆Q = Cp∆T)

(∆W = -P∆V)

PV = RT (Here's R is a constant )

change in V will change in T ( because pressure is also constant)

P∆V = R∆T

Cv∆T = Cp∆T - R∆T

On devIDing by ∆T ,

Cv = Cp - R

Cp - Cv = R

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