Consider a given sample of an ideal gas (C P /C V = γ) having initial pressure P 0 and volume V 0 . (a) The gas is isothermally taken to a pressure P 0 /2 and from there adiabatically to a pressure P 0 /4. Find the final volume. (b) The gas is brought back to its initial state. It is adiabatically taken to a pressure P 0 /2 and from there isothermally to a pressure P 0 /4. Find the final volume.

Question

Philoid · Accepted Answer

Given C_P/C_V = γ, initial pressure P1=P₀ and initial volume V1= V₀

a) Since the gas is isothermally taken to pressure P2=P₀/2

∴

Let P3=P₀/4 and V3 be the pressure and volume after adiabatic compression.

Then,

PV^γ = const.

I.e.

Substituting value of V2=2V₀

(b)Here P1=P₀, P2=P₀/2 and the process is adiabatic. Let V1=V₀ be the initial volume and V2 be the volume after process.

Then,

PV^γ = const.

I.e.

Let P3= P₀/4 and V3 be the pressure and volume after isothermal process Then,