A gas consisting of rigid diatomic molecules was expanded in a polytropic process so that the rate of collisions of the molecules against the vessel's wall did not change. Find the molar heat capacity of the gas in this process is found to be 'xR', the value of x is __________.

Rate of collisions with vessel wall isNC=16n0Vrms=16NV3RTMAs the rate of collisions with vessel wall is constant⇒ NC∝TV= constant ⇒ TV2= Constant     .........(i) As PV=nRT⇒TPV= Constant .........(ii)Hence from (i) and (ii); PV−1= constant .........(iii)Molar heat capacity is given as          C=Rγ−1+R1−n=Cv+R1−n .......(iv)⇒ C=5R2+R1−(−1)=3R