$A$ gas undergoes a change in which its pressure $P$ and volume $V$ are related as $PV^{n} = \text{constant}$, where $n$ is a constant. If the specific heat of the gas in this change is zero, then the value of $n$ is $(\gamma = \text{adiabatic ratio})$.

$A$ vessel contains $0.15 \ \text{m}^3$ of a gas at pressure $8 \ \text{bar}$ and temperature $140^\circ \text{C}$ with $c_p = 3R$ and $c_v = 2R$. It is expanded adiabatically until the pressure falls to $1 \ \text{bar}$. The work done during this process is . . . . . . $\text{kJ}$.

$Assertion :$ Adiabatic expansion is always accompanied by fall in temperature.
$Reason :$ In adiabatic process, volume is inversely proportional to temperature.

$A$ 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:

An ideal gas at a pressure of $1 \text{ atm}$ and temperature of $27^{\circ}C$ is compressed adiabatically until its pressure becomes $8$ times the initial pressure. The final temperature is ..... $^{\circ}C$ (given $\gamma = 3/2$).