In an adiabatic process,if the pressure is increased by $\frac{2}{3}\% $ and the ratio of specific heats $\frac{C_p}{C_v} = \gamma = \frac{3}{2}$,then the volume decreases by about:

The volume of air increases by $5\%$ in its adiabatic expansion. The percentage decrease in its pressure will be ...... $\%$

$A$ monoatomic ideal gas is compressed adiabatically to $12.5 \%$ of its initial volume. If the initial temperature of the gas is $T_1 \ K$ and the final temperature is $xT_1 \ K$,the value of $x$ is:

The amount of work done in an adiabatic expansion from temperature $T$ to ${T_1}$ is

Consider a thermodynamic process where internal energy $U = A P^2 V$ $(A = \text{constant})$. If the process is performed adiabatically, then:

An ideal gas having initial pressure $P$, volume $V$ and temperature $T$ is allowed to expand adiabatically until its volume becomes $4V$, while its temperature falls to $T/2$. If the work done by the gas during the expansion is $\alpha PV$, the value of $\alpha$ is