When a system is taken from state $i$ to state $f$ along the path $iaf$,$Q = 50 \ J$ and $W = 20 \ J$. Along the path $ibf$,$Q = 35 \ J$ and $W = -13 \ J$. For the curved path $fi$,$Q = \dots \ J$.

Helium gas undergoes a cycle $ABCDA$ (consisting of two isochoric and two isobaric lines) as shown in the figure. The efficiency of this cycle is nearly ....... $\%$ (Assume the gas to be an ideal gas).

An insulating cylinder contains $4 \text{ moles}$ of an ideal diatomic gas. When a heat $Q$ is supplied to it, $2 \text{ moles}$ of the gas molecules dissociate. If the temperature of the gas remains constant, then the value of $Q$ is ($R$ - universal gas constant).

One mole of an ideal gas goes from an initial state $A$ to a final state $B$ via two processes: It first undergoes isothermal expansion from volume $V$ to $3V$ and then its volume is reduced from $3V$ to $V$ at constant pressure. The correct $P-V$ diagram representing the two processes is:

When heat $Q$ is supplied to a monoatomic gas at constant pressure,the work done by the gas is:

An ideal gas expands from volume $V_1$ to $V_2$. This may be achieved by either of the three processes: isobaric,isothermal,and adiabatic. Let $\Delta U$ be the change in internal energy of the gas,$Q$ be the quantity of heat added to the system,and $W$ be the work done by the system. Identify which of the following statements is false for $\Delta U$?