In case of an adiabatic process,the correct relation in terms of pressure $p$ and density $\rho$ of a gas is:

$A$ gas having a volume of $1 \ mm^3$ at $1 \ atm$ pressure is compressed from a temperature of $27^{\circ}C$ to $627^{\circ}C$. What will be the final pressure if the process is adiabatic? (For the gas,$\gamma = 1.5$)

Two moles of a gas at a temperature of $327^{\circ} C$ expands adiabatically such that its volume increases by $700 \%$. If the ratio of the specific heat capacities of the gas is $\frac{4}{3}$,then the work done by the gas is (Universal gas constant $= 8.3 \ J \ mol^{-1} \ K^{-1}$) (in $kJ$)

For $1 \text{ mole}$ of an ideal gas,during an adiabatic process,the square of the pressure of a gas is found to be proportional to the cube of its absolute temperature. The specific heat of the gas at constant volume is ($R$ is universal gas constant)

$A$ work of $166.28 \ J$ is done to adiabatically compress one mole of a gas. If the increase in the temperature of the gas is $8^{\circ} C$,the gas is $\left(R=8.314 \ J \ mol^{-1} \ K^{-1}\right)$

Which of the following is true in the case of an adiabatic process,where $\gamma = C_p / C_V$?