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.

Given C_{P}/C_{V} = γ, initial pressure P1=P_{0} and initial volume V1= V_{0}

a) Since the gas is isothermally taken to pressure P2=P_{0}/2

∴

Let P3=P_{0}/4 and V3 be the pressure and volume after adiabatic compression.

Then,

PV^{γ} = const.

I.e.

Substituting value of V2=2V_{0}

(b)Here P1=P_{0}, P2=P_{0}/2 and the process is adiabatic. Let V1=V_{0} be the initial volume and V2 be the volume after process.

Then,

PV^{γ} = const.

I.e.

I.e.

Let P3= P_{0}/4 and V3 be the pressure and volume after isothermal process Then,

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