$A$ graph of pressure versus volume for an ideal gas for different processes is as shown. In the graph,curve $OC$ represents:

An ideal gas at $27^{\circ}C$ is compressed adiabatically to $\frac{8}{27}$ of its original volume. If $\gamma = \frac{5}{3}$,then the rise in temperature is ........ $K$.

$Assertion:$ In adiabatic compression,the internal energy and temperature of the system decrease.
$Reason:$ Adiabatic compression is a slow process.

$A$ diesel engine has a compression ratio of $20:1$. If the initial pressure is $1 \times 10^5 \ Pa$ and the initial volume of the cylinder is $1 \times 10^{-3} \ m^3$,then how much work does the gas do during the compression (in $J$)? (Assume the process as adiabatic) $(C_V=20.8 \ J/mol \ K, \gamma=1.4, (20)^{1.4}=66.3)$

$P-V$ plots for two gases during an adiabatic process are shown in the figure. Plots $(1)$ and $(2)$ correspond respectively to

$A$ monatomic gas at $630 \,K$ expands adiabatically to $27$ times its initial volume. The final temperature of the gas is (in $\,K$)