Correct Answer - Option 3 : Absolute zero temperature

__Explanation:__

For isentropic process:

\(\frac{T_2}{T_1}=\left(\frac{P_2}{P_1}\right)^{\frac{γ -1}{γ}}=\left(\frac{V_1}{V_2}\right)^{{γ -1}}\)

For isothermal process **T**_{1} = T_{2}

\(\frac{T_2}{T_1}=\left(\frac{P_2}{P_1}\right)^{\frac{γ -1}{γ}}\)

\(1=\left(\frac{P_2}{P_1}\right)^{\frac{γ -1}{γ}}\)

\(\frac{γ -1}{γ}=0\)

γ = 1

γ is the ratio of specific heat at constant pressure C_{p} and constant volume C_{v}.

We know that for the difference in specific heat at constant pressure C_{p} and constant volume C_{v} is:

\(C_p-C_v=-T\left(\frac{\partial S}{\partial V}\right)_T\left(\frac{\partial S}{\partial P}\right)_T\)

At Absolute zero temperature dS = 0

∴ C_{p} - C_{v} = 0

C_{p} = C_{v}

\(\frac{C_p}{C_v}=1\)