Question

One mole of an ideal gas is carried through a thermodynamic cycle as shown in the figure. The cyclic process consists of an isochoric, an isothermal and an adiabatic process. Find adiabatic exponent of gas :

• A. $\frac{5}{3}$
• B. $\frac{ln5}{ln3}$
• C. $\frac{4}{3}$
• D. $\frac{ln3}{ln3-\ln 2}$

Answer 1

The correct option is D $\frac{ln3}{ln3-\ln 2}$

Process BC is isothermal.

$⟹PV=constant$

So, $3P_o{V}_1=P_o{V}_o$

$⟹V_1=\frac{V_o}{3}$

Process AC is adiabatic.

$⟹P{V}^{\gamma }=constant$

So, $\left(3P_o\right)(\frac{V_o}{3}{)}^{\gamma }=(\frac{P_o}{2})V_o^{\gamma }$

Or $3^{\gamma -1}=2^{\gamma }$

Or $(\gamma -1)\ln 3=\gamma \ln 2$

$⟹\gamma =\frac{\ln 3}{\ln 3-\ln 2}$