A rigid diatomic gas $\left(\gamma = \dfrac{7}{5}\right)$ is compressed adiabatically to volume $\left(\dfrac{V_i}{32}\right)$, where $V_i$ is the initial volume. The initial temperature of the gas is '$T_i$' K and the final temperature is '$x\,T_i$' K. The value of $x$ is

An ideal rigid diatomic gas $\left(\gamma = \dfrac{7}{5}\right)$ undergoes an adiabatic change . If the relation between temperature and volume is $TV^x = $ constant then the value of x is

Gas at pressure P, temperature T, and volume V is filled in jar A. Another jar B is filled with gas having parameters $2P$, $\dfrac{V}{4}$, $2T$. The ratio of number of molecules of jar B to those of jar A is

A simple pendulum of length $l_1$ has periodic time $2.4$ s. Another simple pendulum of length $l_2 < l_1$, has periodic time $1.8$ s. The periodic time of simple pendulum of length $(l_1 - l_2)$ is nearly