Heat energy of $735\,J$ is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but does not oscillate. The increase in the internal energy of the gas will be $..........\,J$

The efficiency of a thermodynamic cycle $1-2-3-1$ (see picture) is $20\%$ and for another thermodynamic cycle $1-3-4-1$ efficiency is equal to $10\%$. Determine the efficiency $\eta$ (in $\%$) of the thermodynamic cycle $1-2-3-4-1$. The gas is assumed to be ideal.

Which of the following statement$(s)$ is/are true? "Internal energy of an ideal gas ..........."

For a monoatomic ideal gas following the cyclic process $ABCA$ shown in the $U$ vs $\rho$ plot,identify the incorrect option:

$A$ reversible cyclic process for an ideal gas is shown below. Here,$P, V$,and $T$ are pressure,volume,and temperature,respectively. The thermodynamic parameters $q, w, H$,and $U$ are heat,work,enthalpy,and internal energy,respectively.
The correct option$(s)$ is (are):
$(A)$ $q_{AC} = \Delta U_{AC}$ and $W_{AB} = 0$
$(B)$ $W_{BC} = P_2(V_1 - V_2)$ and $q_{BC} = \Delta H_{BC}$
$(C)$ $\Delta H_{CA} < \Delta U_{CA}$ and $q_{AC} = \Delta U_{AC}$
$(D)$ $q_{BC} = \Delta H_{BC}$ and $\Delta H_{CA} > \Delta U_{CA}$

During the melting of a slab of ice at $273 \, K$ at atmospheric pressure,