Question 126: Thermodynamics & KTG

Question

One mole of a monatomic ideal gas undergoes the cyclic process $\mathrm{J} \rightarrow \mathrm{K} \rightarrow \mathrm{L} \rightarrow \mathrm{M} \rightarrow \mathrm{J}$, 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.
[ $\mathcal{R}$ is the gas constant.]

List-I
List-II

(P) Work done in the complete cyclic process
(1) $RT_0 - 4RT_0 \ln 2$

(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) $3RT_0$

(S) Change in the internal energy of the gas in the process MJ
(4) $-2RT_0 \ln 2$

(5) $-3RT_0 \ln 2$

Accepted Answer

$$\begin{aligned}
& \mathrm{J}\left(\mathrm{P}_0, \mathrm{~V}_0, \mathrm{~T}_0ight) \
& K\left(P_0, 3 V_0, 3 T_0ight) \
& \mathrm{M}\left(2 \mathrm{P}_0, \frac{\mathrm{V}_0}{2}, \mathrm{~T}_0ight) \
& \mathrm{L}\left(2 \mathrm{P}_{\circ}, \frac{3 \mathrm{~V}_0}{2}, 3 \mathrm{~T}_0ight) \
& \mathrm{P}_0 \mathrm{~V}_0=\mathrm{nRT}_0 \
& \mathrm{JK} ightarrow 	ext { isobaric } \Rightarrow \mathrm{W}=\mathrm{P}_0\left(2 \mathrm{~V}_0ight)=2 \mathrm{nRT}_0 \
& \Delta \mathrm{U}=\frac{3}{2} \mathrm{nR}\left(2 \mathrm{~T}_0ight)=3 \mathrm{nRT}_0 \
& \mathrm{KL} ightarrow 	ext { isothermal } ightarrow \mathrm{W}=\mathrm{nR}(3 \mathrm{~T}) \ell \mathrm{n}\left(\frac{1}{2}ight)=-3 \mathrm{nRT}_0 \ell \mathrm{n} 2 \
& \Delta \mathrm{U}=0 \Rightarrow \mathrm{Q}=-3 \mathrm{nRT}_0 \ell \mathrm{n} 2 \
& \mathrm{LM} ightarrow 	ext { isobaric }=2 \mathrm{P}_0\left(-\mathrm{V}_0ight)=-2 \mathrm{nRT}_0 \
& \mathrm{MJ} ightarrow 	ext { isothermal } \Rightarrow \mathrm{nRT}_0 \ln 2 ; \Delta \mathrm{U}=0 \
& \mathrm{WD}_{	ext {nes }}=-2 \mathrm{nRT}_0 \ln 2 \
& \mathrm{P} ightarrow 4, \mathrm{Q} ightarrow 3, \mathrm{R} ightarrow 5, \mathrm{~S} ightarrow 2 \
&
\end{aligned}$$

Answer

$\mathrm{P} \rightarrow 1 ; \mathrm{Q} \rightarrow 3 ; \mathrm{R} \rightarrow 5 ; \mathrm{S} \rightarrow 4$

Answer

$\mathrm{P} \rightarrow 4 ; \mathrm{Q} \rightarrow 3 ; \mathrm{R} \rightarrow 5 ; \mathrm{S} \rightarrow 2$

Answer

$\mathrm{P} \rightarrow 4 ; \mathrm{Q} \rightarrow 1 ; \mathrm{R} \rightarrow 2 ; \mathrm{S} \rightarrow 2$

Answer

$\mathrm{P} \rightarrow 2 ; \mathrm{Q} \rightarrow 5 ; \mathrm{R} \rightarrow 3 ; \mathrm{S} \rightarrow 4$

Thermodynamics & KTG

Choose the correct answer: