What is the change in temperature when work is done by a gas in an adiabatic process?

For an adiabatic process with $\gamma = 2.5$,if the volume of a gas is reduced to $1/8$ of its initial volume,what will be the new pressure $P'$ in terms of the initial pressure $P$?

Air is filled in a motor tube at $27^{\circ}C$ and at a pressure of $8$ atmospheres. The tube suddenly bursts,then the temperature of the air is $[\text{Given } \gamma \text{ of air} = 1.5]$.

An ideal gas at $27^{\circ} C$ is compressed adiabatically to $8/27$ of its original volume. If the ratio of specific heats is $\gamma = 5/3$,then the rise in temperature of the gas is: (in $K$)

An ideal gas undergoes a process $A \rightarrow B \rightarrow C \rightarrow A$ cycle. The process $A \rightarrow B$ is adiabatic. Calculate the work done in the process $A \rightarrow B$.

In an adiabatic change,the pressure $P$ and temperature $T$ of a monoatomic gas are related by the relation $P \propto T^C$,where $C$ equals