The $P-V$ diagram for two adiabatic processes is given. Curves $1$ and $2$ correspond to:

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:

In the following $P-V$ diagram, two adiabatics cut two isothermals at temperatures $T_1$ and $T_2$. The value of $\frac{V_a}{V_d}$ will be

In which thermodynamic process is there no exchange of heat between the system and the surroundings?

$A$ gas is suddenly compressed to $1/4$ th of its original volume at normal temperature. The increase in its temperature is ....... $K$ $(\gamma = 1.5)$

$A$ 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 $P_{2}$?