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\( .1 \) a thermodynamics process on an ideal monatomic a as, the infinitesimal heat absorbed by the gas is given y \( T \Delta X \), where \( T \) is temperature of the system and \( \Delta \mathrm{X} \) is the infinitesimal change in a thermodynamic quantity \( \mathrm{X} \) of the system. For a mole of monatomic ideal gas \( \mathrm{X}= \)
\( P \) \( { }^{3} \mathrm{R} \) in \( \left(\frac{\mathrm{T}}{\mathrm{T}_{\mathrm{A}}}\right)+\mathrm{R} \) In \( \left(\frac{\mathrm{V}}{\mathrm{V}_{\mathrm{A}}}\right) \). Here, \( \mathrm{R} \) is gas constant, \( \mathrm{V} \)

W volume of gas, \( \mathrm{T}_{\mathrm{A}} \) and \( \mathrm{V}_{\mathrm{A}} \) are constants. he List-I below gives some quantities involved and ist-II gives some possible values of these quantities.
List-I List-II
(I) Work done by the system in process
\( 1 \rightarrow 2 \rightarrow 3 \)
(P) \( \frac{1}{3} \mathrm{RT}_{6} \ln 2 \)
(II) Change in internal energy in process
\( 1 \rightarrow 2 \rightarrow 3 \)
(Q) \( \frac{1}{3} R T_{e} \)
III) Heat absorbed by the system in process
(IV) Heat absorbed by the system in process
(S) \( \frac{4}{3} \mathrm{RT}_{0} \)
\( \frac{1}{3} R T_{0}(3+\ln 2) \)
(U) \( \frac{5}{6} \mathrm{RT}_{6} \)
the process on one mole of monatomic ideal gas is an
Hown is as shown in the TV-diagram with \( \mathrm{P}_{0} \mathrm{~V}_{0}=\frac{1}{3} \mathrm{RT}_{0} \),
[JEEAdvanced-2019]
A) \( \mathrm{I} \rightarrow \mathrm{S}, \mathrm{II} \rightarrow \mathrm{T} \), III \( \rightarrow \) Q, IV \( \rightarrow \mathrm{U} \)
(B) \( \mathrm{I} \rightarrow \mathrm{P}, \mathrm{II} \rightarrow \mathrm{R}, \mathrm{III} \rightarrow \mathrm{T}, \mathrm{IV} \rightarrow \mathrm{S} \) \( \mathrm{IO} \mathrm{I} \rightarrow \mathrm{P} \), II \( \rightarrow \) T, III \( \rightarrow \) Q. IV \( \rightarrow \) T
\( \rightarrow \) P \( ) \rightarrow \mathrm{P}, \mathrm{II} \rightarrow \mathrm{R}, \mathrm{III} \rightarrow \mathrm{T}, \mathrm{IV} \rightarrow \mathrm{P} \)
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