Slope of isotherm for a gas (having $\gamma=\frac{5}{3}$ ) is $3 \times 10^5 \,N / m ^2$. If the same gas is undergoing adiabatic change then adiabatic elasticity at that instant is ........... $\times 10^5 N / m ^2$

Starting with the same initial conditions, an ideal gas expands from volume $V_{1}$ to $V_{2}$ in three different ways. The work done by the gas is $W_{1}$ if the process is purely isothermal. $W _{2}$. if the process is purely adiabatic and $W _{3}$ if the process is purely isobaric. Then, choose the coned option

$Assertion :$ Air quickly leaking out of a balloon becomes cooler.
$Reason :$ The leaking air undergoes adiabatic expansion.

Graph $A-B$ is an adiabatic curve. Choose the correct statement

An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes $32$ times of its initial value. If the final pressure of gas is $128$ atmosphers, the value of $\gamma$ the gas is

The volume of a gas is reduced adiabatically to $\frac{1}{4}$ of its volume at $27°C$, if the value of $\gamma = 1.4,$ then the new temperature will be