For an adiabatic expansion of a perfect gas,the value of $\frac{\Delta P}{P}$ is equal to

Consider a cycle tyre being filled with air by a pump. Let $V$ be the volume of the tyre (fixed) and at each stroke of the pump $\Delta V$ ( < < V) of air is transferred to the tube adiabatically. What is the work done when the pressure in the tube is increased from $P_1$ to $P_2$?

In an adiabatic expansion,the product of pressure and volume:

$A$ gas at $37^{\circ} C$ is compressed adiabatically to half of its volume. What is the final temperature of the gas (in $^{\circ} C$)? (Ratio of specific heat capacities of the gas is $1.5$)

Specific heat of a gas undergoing adiabatic change is

The initial pressure and volume of a given mass of an ideal gas (with $\frac{C_{p}}{C_{V}}=\gamma$),taken in a cylinder fitted with a piston,are $p_{0}$ and $V_{0}$ respectively. At this stage,the gas has the same temperature as that of the surrounding medium,which is $T_{0}$. It is adiabatically compressed to a volume equal to $\frac{V_{0}}{2}$. Subsequently,the gas is allowed to come to thermal equilibrium with the surroundings. What is the heat released to the surrounding?