The bulk modulus of a gas is defined as $B = -V (dp / dV)$. For an adiabatic process,the variation of $B$ is proportional to $p^n$. For an ideal gas,$n$ is:

The initial pressure and volume of an ideal gas are $P_0$ and $V_0$. The final pressure of the gas when the gas is suddenly compressed to volume $\frac{V_0}{4}$ will be (Given $\gamma =$ ratio of specific heats at constant pressure and at constant volume).

$A$ monoatomic ideal gas is compressed adiabatically to $\left(\frac{1}{27}\right)$ of its initial volume. If the initial temperature of the gas is $T \ K$ and the final temperature is $xT \ K$, the value of $x$ is:

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

In an adiabatic process $90 \ J$ of work is done on the gas. The change in internal energy of the gas is ....... $J$.

During an adiabatic process,the volume of a gas is found to be inversely proportional to the cube of its temperature. The ratio of $\frac{C_p}{C_v}$ for the gas is