One mole of an ideal gas is taken along the process in which PV^x = constant. The graph shown represents the variation of molar heat capacity of such a gas with respect to x. The value of c' and x', respectively, are given by : 

\(\frac{5}{2}R, \frac{5}{3}\)

At x = \(\infty\), C = \(\frac{3}{2}R\)

from \(PV^x =\) constant and \(P^{1/x}V =\) another constant

So, at : x = \(\infty\), V = constant

Hence, \(C =C_v = \frac{3}{2}R\) and then \(C_P = C_V + R = \frac{5}{2}R\)

at x = 0, P = constant and C = C'

Hence, \(C' = C_P = \frac{5}{2}R\) x = x', C = 0, So the process is adiabatic,

Thus, x' = \(\frac{C_P}{C_V} =\) 5