Question

Show that Cp=Cv+R

Answer 1

Consider one mole of ideal gas enclosed in a cylinder fitted with Mass less piston

According to first law of thermodynamics

dU=dq + dW

At constant volume ( isochoric)

dv=0

dU=dq

dq is also equal to nC_vdT

[dU=nC_vdT]

At constant pressure

dH=dU + PdV ,. dq=dU+PdV

dH=dq

[dH=nC_pdT]

dH=dU+PdV

For an ideal gas equation

PdV=nRdT

dH=dU+nRdT

nC_pdT=nC_vdT+nRdT

C_p=C_v+R