SSC JE Mechanical Engineering 11 Oct 2020 Shift 1 Papers

For isentropic or reversible adiabatic process the P-V-T relation is given by
$\frac{{\mathit{T}}_2}{{\mathit{T}}_1}={\left(\frac{{\mathit{V}}_1}{{\mathit{V}}_2}\right)}^{\mathrm{\gamma }-1}={\left(\frac{{\mathit{P}}_2}{{\mathit{P}}_1}\right)}^{\frac{\mathrm{\gamma }-1}{\mathrm{\gamma }}}$
or $\mathit{P}=\mathit{K}{\mathit{T}}^{\mathrm{\gamma }∕\mathrm{\gamma }-1}$
The given relation for the isentropic process in the question is
$\mathit{P}=\mathit{K}{\mathit{T}}^{5∕2}$
Comparing the above relationship with the standard relation of the isentropic process we will get,
$\frac{\mathrm{\gamma }}{\mathrm{\gamma }-1}=\frac{5}{2}$
$2\mathrm{\gamma }=5\mathrm{\gamma }-5,3\mathrm{\gamma }=5$ or $\mathrm{\gamma }=5∕3$