Question

Derive a relationship between cp and cv for an ideal gas

Answer 1

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Answer 2

Answer

We know that,

H = U + PV

by differentiating above equation with respect to temperature at constant pressure we get,

dH/dT = dU/dT + P dV/dT ————(1)

for one mole of gas,

PV = RT

differentiating this , temperature at constant pressure,we get

PdV/dT = R

dH/dT =Cp , dU/dT = Cv and PdV/dT=R hence equation (1) becomes.

Cp = Cv + R

Cp-Cv =R

this relation is known as Meyer’s relation