An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and then compressed to original volume $V_1$ adiabatically. Initial pressure is $P_1$ and final pressure is $P_3$. The total work done is $W$. Then
$P_3 > P_1, W > 0$
$P_3 < P_1, W < 0$
$P_3 > P_1, W < 0$
$P_3 = P_1, W = 0$
Which of the following graphs correctly represents the variation of $\beta = - \left( {\frac{{dV}}{{dP}}} \right)/V$ with $P$ for an ideal gas at constant temperature ?
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $C_P / C_V$ for the gas is
A monoatomic gas is supplied heat $Q$ very slowly keeping the pressure constant. The work done by the gas will be
$Assertion :$ The isothermal curves intersect each other at a certain point.
$Reason :$ The isothermal changes takes place rapidly, so the isothermal curves have very little slope.
$P-V$ diagram of $2\,g$ of $He$ gas for $A \to B$ process is shown. What is the heat given to the gas ?