$A$ gas is compressed from a volume of $2 \,m^3$ to a volume of $1 \,m^3$ at a constant pressure of $100 \,N m^{-2}$. Then it is heated at constant volume by supplying $150 \,J$ of energy. As a result,the internal energy of the gas

$A$ monoatomic gas at a pressure $P$,having a volume $V$ expands isothermally to a volume $4V$ and then adiabatically to volume $16V$. The final pressure of the gas is (Take $\gamma = \frac{5}{3}$)

An ideal gas,initially in state $(P_{12}, V_1, T_1)$ is expanded isobarically to $(P_{12}, V_2, T_2)$,then adiabatically to $(P_{34}, V_3, T_3)$. It is then contracted isobarically to $(P_{34}, V_4, T_4)$ and finally adiabatically back to the initial state. The efficiency of this cycle is

Column-$I$ shows graphs of thermodynamic processes, and column-$II$ contains information about various thermodynamic variables. Match column-$I$ with the information in column-$II$.

Column-$I$	Column-$II$
$(A)$ $PV$ vs $V$ (Isothermal expansion)	$(P)$ $W$ > 0
$(B)$ $P$ vs $T$ (Isochoric heating)	$(Q)$ $W$ < 0
$(C)$ $P$ vs $V$ (Isobaric expansion)	$(R)$ $\Delta Q$ > 0
$(D)$ $V$ vs $T$ (Isobaric compression)	$(S)$ $\Delta U$ > 0
	$(T)$ $\Delta U$ < 0

Three processes compose a thermodynamic cycle shown in the $PV$ diagram. Process $1\rightarrow 2$ takes place at constant temperature. Process $2\rightarrow 3$ takes place at constant volume,and process $3\rightarrow 1$ is adiabatic. During the complete cycle,the total amount of work done is $10\,J$. During process $2\rightarrow 3$,the internal energy decreases by $20\,J$ and during process $3\rightarrow 1$,$20\,J$ of work is done on the system. How much heat is added to the system during process $1\rightarrow 2$ (in $,J$)?

An ideal monatomic gas of $n$ moles is taken through a cycle $W-X-Y-Z-W$ consisting of consecutive adiabatic and isobaric quasi-static processes,as shown in the schematic $V-T$ diagram. The volumes of the gas at $W, X,$ and $Y$ points are $64 \ cm^3, 125 \ cm^3,$ and $250 \ cm^3,$ respectively. If the absolute temperature of the gas $T_W$ at point $W$ is such that $nRT_W = 1 \ J$ ($R$ is the universal gas constant),then the amount of heat absorbed (in $J$) by the gas along the path $XY$ is $.....$