An ideal gas,undergoing adiabatic change,has which of the following pressure-temperature relationships?

In an adiabatic process,the density of a diatomic gas becomes $32$ times its initial value. The final pressure of the gas is found to be $n$ times the initial pressure. The value of $n$ is

The phenomenon of sound propagation in air is

During an adiabatic process,the pressure of the gas is found to be proportional to the cube of its absolute temperature. The ratio $C_P/C_V = \gamma$ for the gas is:

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.