When an ideal gas is heated at constant pressure,what percentage of the heat supplied is used to perform external work? $(\gamma = 5/3)$

An ideal gas undergoes a thermodynamic cycle as shown in the figure. Which of the following graphs represents the same cycle?

An ideal monoatomic gas is taken through a process $dQ = 2dU$. The molar heat capacity for the process is:

The figure shows a cylindrical adiabatic container of total volume $2V_0$ divided into two equal parts by a conducting piston (which is free to move). Each part contains an identical gas at pressure $P_0$. Initially,the temperature of the left and right parts is $4T_0$ and $T_0$ respectively. An external force is applied on the piston to keep it at rest. Find the value of the external force required when thermal equilibrium is reached. ($A =$ Area of the piston)

$List-I$ describes thermodynamic processes in four different systems. $List-II$ gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.

$List-I$	$List-II$
$(I)$ $10^{-3} \, kg$ of water at $100^{\circ} C$ is converted to steam at the same temperature, at a pressure of $10^5 \, Pa$. The volume of the system changes from $10^{-6} \, m^3$ to $10^{-3} \, m^3$. Latent heat of water $= 2250 \, kJ/kg$.	$(P)$ $2 \, kJ$
$(II)$ $0.2 \, moles$ of a rigid diatomic ideal gas with volume $V$ at temperature $500 \, K$ undergoes an isobaric expansion to volume $3V$. Assume $R = 8.0 \, J \, mol^{-1} \, K^{-1}$.	$(Q)$ $7 \, kJ$
$(III)$ One mole of a monatomic ideal gas is compressed adiabatically from volume $V = 1/3 \, m^3$ and pressure $2 \, kPa$ to volume $V/8$.	$(R)$ $4 \, kJ$
$(IV)$ Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 \, kJ$ of heat and undergoes isobaric expansion.	$(S)$ $5 \, kJ$
	$(T)$ $3 \, kJ$

Which one of the following options is correct?

What are the limitations of the first law of thermodynamics?