$A$ gas does $4.5 \,J$ of external work during adiabatic expansion. If its temperature falls by $2 \,K$, then its internal energy will be

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.

$A$ gas is suddenly compressed to one fourth of its original volume. What will be its final pressure,if its initial pressure is $P$?

An ideal gas initially at $0^{\circ} C$ temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is $3/2$, the change in temperature due to the thermodynamics process is . . . . . . $K.$

Specific heat of a gas undergoing adiabatic change is

$A$ polyatomic gas follows a law $T^2 V^\alpha = \text{constant}$. Find $\alpha$ for which the heat exchange of gas in the process becomes zero.