Match the thermodynamic processes taking place in a system with the correct conditions. In the table: $\Delta Q$ is the heat supplied,$\Delta W$ is the work done and $\Delta U$ is change in internal energy of the system.

Process	Condition
$(I)$ Adiabatic	$(A) \Delta W = 0$
$(II)$ Isothermal	$(B) \Delta Q = 0$
$(III)$ Isochoric	$(C) \Delta U \neq 0, \Delta W \neq 0, \Delta Q \neq 0$
$(IV)$ Isobaric	$(D) \Delta U = 0$

One mole of an ideal gas undergoes two different cyclic processes $I$ and $II$,as shown in the $P-V$ diagrams below. In cycle $I$,processes $a, b, c$ and $d$ are isobaric,isothermal,isobaric and isochoric,respectively. In cycle $II$,processes $a^{\prime}, b^{\prime}, c^{\prime}$ and $d^{\prime}$ are isothermal,isochoric,isobaric and isochoric,respectively. The total work done during cycle $I$ is $W_I$ and that during cycle $II$ is $W_{II}$. The ratio $W_I / W_{II}$ is . . . .

$A$ bubble containing $8$ moles of Helium is submerged at a certain depth in water. When the temperature of the water increases by $30 \ ^\circ C$,how much heat in $J$ is added during the expansion of the Helium bubble?

$A$ gas undergoes a change of state during which $100 \ J$ of heat is supplied to it and it does $20 \ J$ of work. The system is brought back to its original state through a process during which $20 \ J$ of heat is released by the gas. The work done by the gas in the second process is ....... $J$

An ideal gas undergoes a cyclic process as shown in the density-pressure graph. During the process $AB$, the work done $|W_{AB}| = 70\,J$. During the process $BC$, the gas absorbs $150\,J$ of heat. During the process $CA$, the gas undergoes expansion and does $210\,J$ of work. Which of the following statements is correct?

The cycle shown in the figure represents an engine (the engine consists of one mole of gas in a cylinder with a piston). $A$ to $B$ is isochoric,$B$ to $C$ is isothermal,$C$ to $D$ is isochoric,and $D$ to $A$ is isothermal. Also,$V_C = V_D = 2V_A = 2V_B$.
$(a)$ In which part of the cycle is heat supplied to the engine from the outside?
$(b)$ In which part of the cycle can the engine give energy to its surroundings?
$(c)$ How much work is done by the engine during one cycle? Give your answer in terms of $P_A, P_B$ and $V_A$.
$(d)$ What is the efficiency of the engine? (For the gas,$\gamma = 5/3$,and for one mole,$C_V = 3/2 R$)