Explanation:
For adiabatic process,
\(T{V^{\gamma - 1}} = \;{\text{constant}}\)
\(\therefore \quad \frac{{{T_2}}}{{{T_1}}} = {\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^{\gamma - 1}}\,\,\,\,\,\,\,\,\,\,\,(1)\)
But, \({V_2} = \frac{{{V_1}}}{9}\) and \({T_2} = \sqrt 3 \quad {T_1}\)
\(\therefore \quad \sqrt 3 = {(9)^{\gamma - 1}}\)
\(\therefore \quad {(9)^{\frac{1}{4}}} = {(9)^{\gamma - 1}}\)
\(\therefore \gamma - 1 = \frac{1}{4}\)
\(\therefore \gamma = 1 + \frac{1}{4} = \frac{5}{4}\)
Also for adiabatic process,\(P{V^\gamma } = \) constant
\(\therefore \quad P{V^{\frac{5}{4}}} = \) constant
\(\therefore \quad x = \frac{5}{4} = 1.25\)