At $27^\circ C$,a gas is suddenly compressed such that its pressure becomes $1/8$th of the original pressure. The temperature of the gas will be $(\gamma = 5/3)$.

One mole of an ideal gas $(C_p/C_v = \gamma)$ at absolute temperature $T_1$ is adiabatically compressed from an initial pressure $P_1$ to a final pressure $P_2$. The resulting temperature $T_2$ of the gas is given by

One mole of an ideal gas expands adiabatically at constant pressure such that its temperature $T \propto \frac{1}{\sqrt{V}}$. The value of $\gamma$ for the gas is $(\gamma = \frac{C_p}{C_v}, V = \text{Volume of the gas})$

Identify the characteristics of an adiabatic process in a monoatomic gas.
$(A)$ Internal energy is constant.
$(B)$ Work done in the process is equal to the change in internal energy (in magnitude).
$(C)$ The product of temperature and volume is a constant.
$(D)$ The product of pressure and volume is a constant.
$(E)$ The work done to change the temperature from $T_1$ to $T_2$ is proportional to $(T_2 - T_1)$.
Choose the correct answer from the options given below.

In an adiabatic change,the pressure $P$ and temperature $T$ of a diatomic gas are related by the relation $P \propto T^C$,where $C$ is equal to:

The pressure in the tyre of a car is four times the atmospheric pressure at $300 \ K$. If this tyre suddenly bursts,its new temperature will be $(\gamma = 1.4)$.