For an adiabatic process,the pressure and temperature of a monoatomic gas are related as $P \propto T^{c}$. Then,$c = $.......

If the pressure in an adiabatic process increases by $\frac{2}{3}\%$,then the percentage decrease in volume will be ....... . Assume $C_P/C_V = 3/2$.

$A$ monoatomic gas having $\gamma = 5/3$ is stored in a thermally insulated container and the gas is suddenly compressed to $(1/8)^{th}$ of its initial volume. The ratio of final pressure to initial pressure is: ($\gamma$ is the ratio of specific heats of the gas at constant pressure and at constant volume).

$A$ diatomic ideal gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume. If the initial temperature of the gas is $T_1$ (in Kelvin) and the final temperature is $a T_1$,the value of $a$ is

$Assertion :$ Air quickly leaking out of a balloon becomes cooler.
$Reason :$ The leaking air undergoes adiabatic expansion.

The equation of state of $n$ moles of a non-ideal gas can be approximated by the equation $\left(p+\frac{n^2 a}{V^2}\right)(V-n b)=n R T$,where $a$ and $b$ are constant characteristics of the gas. Which of the following can represent the equation of a quasistatic adiabat for this gas? (Assume that $C_V$,the molar heat capacity at constant volume,is independent of temperature.)