Five moles of Hydrogen gas initially at $STP$ is compressed adiabatically so that its temperature becomes $673 \, K$. The increase in internal energy of the gas is $(R=8.3 \, J \, mol^{-1} \, K^{-1}, \gamma=1.4$ for diatomic gas$)$ (in $kJ$)

The following figure shows an adiabatic cylindrical container of volume $V_0$ divided by an adiabatic smooth piston (area of cross-section = $A$) into two equal parts. An ideal gas $(C_P/C_V = \gamma)$ is at pressure $P_1$ and temperature $T_1$ in the left part,and a gas at pressure $P_2$ and temperature $T_2$ is in the right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose $x$ = displacement of the piston):

$A$ gas has pressure $P$ and volume $V$. If the gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume,what will be the new pressure? (Given: $(32)^{1.4} = 128$)

Jet aircrafts fly at altitudes above $30000 \,ft$, where the air is very cold at $-40^{\circ} C$ and the pressure is $0.28 \,atm$. The cabin is maintained at $1 \,atm$ pressure by means of a compressor which exchanges air from outside adiabatically. In order to have a comfortable cabin temperature of $25^{\circ} C$, we will require in addition

The volume of a gas is reduced adiabatically to $(1/4)^{th}$ of its initial volume. If the initial temperature is $27\,^{\circ}C$ and $\gamma = 1.4$, the new temperature is:

In an adiabatic process,which of the following statements is true?