One mole of a monatomic ideal gas undergoes the cyclic process $J \rightarrow K \rightarrow L \rightarrow M \rightarrow J$,as shown in the $P - T$ diagram. Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option. [$R$ is the gas constant]
$List-I$$List-II$
$(P)$ Work done in the complete cyclic process$(1)$ $R T_0 - 4 R T_0 \ln 2$
$(Q)$ Change in the internal energy of the gas in the process $JK$$(2)$ $0$
$(R)$ Heat given to the gas in the process $KL$$(3)$ $3 R T_0$
$(S)$ Change in the internal energy of the gas in the process $MJ$$(4)$ $-2 R T_0 \ln 2$
$(5)$ $-3 R T_0 \ln 2$

  • A
    $P \rightarrow 1 ; Q \rightarrow 3 ; R \rightarrow 5 ; S \rightarrow 4$
  • B
    $P \rightarrow 4 ; Q \rightarrow 3 ; R \rightarrow 5 ; S \rightarrow 2$
  • C
    $P \rightarrow 4 ; Q \rightarrow 1 ; R \rightarrow 2 ; S \rightarrow 2$
  • D
    $P \rightarrow 2 ; Q \rightarrow 5 ; R \rightarrow 3 ; S \rightarrow 4$

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In changing the state of a gas adiabatically from an equilibrium state $A$ to another equilibrium state $B$,an amount of work equal to $22.3 \; J$ is done on the system. If the gas is taken from state $A$ to $B$ via a process in which the net heat absorbed by the system is $9.35 \; cal$,how much is the net work done (in $J$) by the system in the latter case? (Take $1 \; cal = 4.19 \; J$)

$A$ cylinder made of perfectly non-conducting material,closed at both ends,is divided into two equal parts by a heat-proof piston. Both parts of the cylinder contain the same mass of a gas at a temperature $t_0 = 27^{\circ}C$ and pressure $P_0 = 1 \text{ atm}$. If the gas in one of the parts is slowly heated to $t = 57^{\circ}C$ while the temperature of the first part is maintained at $t_0$,the distance moved by the piston from the middle of the cylinder will be $x \text{ cm}$. Find $x$ (total length of the cylinder $= 84 \text{ cm}$).

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One mole of a monatomic ideal gas is taken along two cyclic processes $E \rightarrow F \rightarrow G \rightarrow E$ and $E \rightarrow F \rightarrow H \rightarrow E$ as shown in the $PV$ diagram. The processes involved are purely isochoric,isobaric,isothermal,or adiabatic. Match the paths in List-$I$ with the magnitudes of the work done in List-$II$ and select the correct answer using the codes given below the lists.
List-$I$List-$II$
$P. \quad G \rightarrow E$$1. \quad 160 P_0 V_0 \ln 2$
$Q. \quad G \rightarrow H$$2. \quad 36 P_0 V_0$
$R. \quad F \rightarrow H$$3. \quad 24 P_0 V_0$
$S. \quad F \rightarrow G$$4. \quad 31 P_0 V_0$

Codes: $P \quad Q \quad R \quad S$

Draw $P-V$ curves for isothermal and adiabatic processes of an ideal gas.

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

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