$A$ heat engine is involved with an exchange of heat of $1915\, J,$ $-40\, J,$ $+125\, J,$ and $-Q\, J$ during one cycle,achieving an efficiency of $50.0 \%$. The value of $Q$ is ....... $J$.

Consider the following volume-temperature $(V-T)$ diagram for the expansion of $5$ moles of an ideal monoatomic gas. Considering only $P-V$ work is involved,the total change in enthalpy (in Joule) for the transformation of state in the sequence $X \rightarrow Y \rightarrow Z$ is $\qquad$ [Use the given data: Molar heat capacity of the gas for the given temperature range,$C_{v,m} = 12 \ J \ K^{-1} \ mol^{-1}$ and gas constant,$R = 8.3 \ J \ K^{-1} \ mol^{-1}$]

When $80 \ J$ of heat is supplied to a gas at constant pressure,if the work done by the gas is $20 \ J$,then the ratio of the specific heat capacities of the gas is

$A$ cyclic process $ABCA$ is shown in the $PT$ diagram. When represented on a $PV$ diagram,it would be:

One mole of an ideal gas at initial temperature $T$ undergoes a quasi-static process during which the volume $V$ is doubled. During the process,the internal energy $U$ obeys the equation $U = a V^3$,where $a$ is a constant. The work done during this process is

Which of the following statements is correct?