$A$ monoatomic gas is stored in a thermally insulated container and the gas is suddenly compressed to $(\frac{1}{8})^{\text{th}}$ of its initial volume. The ratio of final pressure to initial pressure is (in $:1$)

$A$ spherical bubble inside water has radius $R$. Take the pressure inside the bubble and the water pressure to be $p_0$. The bubble now gets compressed radially in an adiabatic manner so that its radius becomes $(R-a)$. For $a \ll R$,the magnitude of the work done in the process is given by $(4 \pi p_0 R a^2) X$,where $X$ is a constant and $\gamma = C_p / C_V = 41 / 30$. The value of $X$ is:

In an adiabatic change,the pressure and temperature of a monoatomic gas are related by the relation $p \propto T^{C}$,where $C$ is equal to

$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas column before and after expansion respectively,then $T_1/T_2$ is given by

In an adiabatic process,the initial and final temperatures of $1 \, mol$ of an ideal gas are $T_1$ and $T_2$ respectively. The change in internal energy of the gas is .......

$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. $L_1$ and $L_2$ are the lengths of the gas columns before and after the expansion,respectively. The ratio $T_2 / T_1$ is