A gas is suddenly compressed to one fourth of its original volume. What will be its final pressure, if its initial pressure is $P$

Areversible adiabatic path on a $P-V$ diagram for an ideal gas passes through stateAwhere $P=0$.$7\times 10^5 \,\,N/ m^{-2}$ and $v = 0.0049 \,\,m^3$. The ratio of specific heat of the gas is $1.4$. The slope of path at $A$ is :

Three samples of the same gas $A, B$ and $C(\gamma = 3/2)$ have initially equal volume. Now the volume of each sample is doubled. The process is adiabatic for $A$ isobaric for $B $ and isothermal for $C$. If the final pressures are equal for all three samples, the ratio of their initial pressures are

Two cylinders $A$ and $B$ of equal capacity are connected to each other via a stop cock. A contains an Ideal gas at standard temperature and pressure. $B$ is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is :

The pressure $P_{1}$ and density $d_{1}$ of diatomic gas $\left(\gamma=\frac{7}{5}\right)$ changes suddenly to $P _{2}\left(> P _{1}\right)$ and $d _{2}$ respectively during an adiabatic process. The temperature of the gas increases and becomes $......$ times of its initial temperature.$\left(\right.$ given $\left.\frac{ d _{2}}{ d _{1}}=32\right)$

In which of the following processes, heat is neither absorbed nor released by a system ?