Question

If the ratio of specific heat of a gas at constant pressure to that at constant volume is γ, the change in internal energy of a mass of gas, when the volume changes from V to 2V at constant pressure P, is

(a) PV/(γ - 1)

(b) PV

(c) R/(γ - 1)

(d) γPV/(γ - 1)

Answer 1

Correct option (a) PV/(γ - 1)

Explanation:

Answer 2

Option (A) is correct

Explanation

Let the number of moles of gas taken is n

So by ideal gas equation ,PV=nRT

As the volume changes from V to 2V. Where pressure P remaining Constant. We can say
∆V=V and
P∆V=nR∆T

=>PV=nR∆T.....(1), where ∆T represents the rise in temperature in absolute scale.

Again change in internal energy

∆U=nCv∆T.......(2)

By (1) and (2)

∆U=Cv×PV/R=(CvPV)/(Cp-Cv)

=PV/(Cp/Cv-1)=PV/(¥-1), where Cp/Cv=¥