Two moles of a monoatomic ideal gas is confined in a container and is heated such that its temperature increases by $10\,^{\circ}C$. The approximate change in its internal energy is ..... $J$. $(R = 8.31\, J/mol\cdot K)$

An ideal gas is taken from state $1$ to state $2$ through optional paths $A, B, C$ and $D$ as shown in the $P-V$ diagram. Let $Q, W$ and $\Delta U$ represent the heat supplied,work done,and change in internal energy of the gas,respectively. Then:

$A$ monatomic gas at a pressure $P$, having a volume $V$, expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is (Take $\gamma = 5/3$)

Given $P_A = 3 \times 10^4 \, Pa$,$P_B = 8 \times 10^4 \, Pa$,$V_A = 2 \times 10^{-3} \, m^3$,and $V_D = 5 \times 10^{-3} \, m^3$. An ideal gas absorbs $600 \, J$ of heat in the process $AB$ and $200 \, J$ of heat in the process $BC$. Find the change in internal energy between $A$ and $C$ in $J$.

$A$ process is shown in the diagram. Which of the following curves may represent the same process?

In Column-$I$ devices and in Column-$II$ efficiency are given. Match them appropriately:

Column-$I$	Column-$II$
$(a)$ Heat engine	$(i)$ $\eta = \frac{Q_2}{Q_1 - Q_2}$
$(b)$ Heat pump	$(ii)$ $\eta = \frac{Q_1 - Q_2}{Q_1}$
	$(iii)$ $\eta = \frac{T_1 - T_2}{T_1}$