One mole of an ideal gas $\left( {\frac{{{C_p}}}{{{C_v}}} = Y} \right)$ heated by law $P = \alpha V$ where $P$ is pressure of gas, $V$ is volume, $\alpha $ is a constant. What is the molar heat capacity of gas in the process
$C = \frac{R}{{\gamma - 1}}$
$C = \frac{{\gamma R}}{{\gamma - 1}}$
$C = \frac{R}{2}\frac{{\left( {\gamma - 1} \right)}}{{\left( {\gamma + 1} \right)}}$
$C = \frac{R}{2}\frac{{\left( {\gamma + 1} \right)}}{{\left( {\gamma - 1} \right)}}$
A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then
A long cylindrical pipe of radius $20 \,cm$ is closed at its upper end and has an airtight piston of negligible mass as shown. When a $50 \,kg$ mass is attached to the other end of piston, it moves down by a distance $\Delta l$ before coming to equilibrium. Assuming air to be an ideal gas, $\Delta l / l$ (see figure) is close to $\left(g=10 \,m / s ^2\right.$, atmospheric pressure is $10^5 \,Pa$ ),
An ideal gas expands in such a way that $PV^2 =$ constant throughout the process
A thermodynamic system is taken through the cycle $PQRSP$ process. the net work done by the system is...... $J$
An insulated box containing a diatomic gas of molar mass $m$ is moving with velocity $v$. The box is suddenly stopped. The resulting change in temperature is :-