If during an adiabatic process the pressure of a mixture of gases is found to be proportional to the square of its absolute temperature,the ratio of $C_p / C_v$ for the mixture of gases is .........

In a thermodynamic process, helium gas obeys the law $TP^{-2/5} = \text{constant}$. The heat given to the gas when the temperature of $2$ moles of the gas is raised from $T$ to $4T$ ($R$ is the universal gas constant) is:

$A$ bicycle tire tube is inflated using a pump. Assume the volume of the tube $V$ is constant and in each stroke,an amount of air $\Delta V$ is pushed into the tube under an adiabatic process. What is the work done to increase the pressure in the tube from $P_{1}$ to $P_{2}$?

In a thermodynamic process,there is no exchange of heat between the system and surroundings. Then the thermodynamic process is

Five moles of hydrogen initially at $STP$ is compressed adiabatically so that its temperature becomes $673 \, K$. The increase in internal energy of the gas, in kilo joule is $(R=8.3 \, J/mol-K; \gamma=1.4$ for diatomic gas$)$

When a gas is compressed adiabatically by a piston in a cylinder,the work done on the gas is found to be $1.5 \times 10^{4} \, J$. During this process: