$A$ monoatomic ideal gas is compressed adiabatically to $12.5 \%$ of its initial volume. If the initial temperature of the gas is $T_1 \ K$ and the final temperature is $xT_1 \ K$,the value of $x$ 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,$\gamma = 1.5$)

In an adiabatic process,the state of a gas is changed from $(P_1, V_1, T_1)$ to $(P_2, V_2, T_2)$. Which of the following relations is correct?

$A$ polyatomic gas $(\gamma = 4/3)$ is compressed to $(1/8)^{\text{th}}$ of its initial volume adiabatically. If its initial pressure is $P_0$,what will be its new pressure (in $P_0$)?

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

The relation between volume $(V)$ and absolute temperature $(T)$ of a gas in an adiabatic process is