$List I$ describes thermodynamic processes in four different systems. $List II$ gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.

$List-I$ $List-II$

($I$) $10^{-3} kg$ of water at $100^{\circ} C$ is converted to steam at the same temperature, at a pressure of $10^5 Pa$. The volume of the system changes from $10^{-6} m ^3$ to $10^{-3} m ^3$ in the process. Latent heat of water $=2250 kJ / kg$. ($P$) $2 kJ$

($II$) $0.2$ moles of a rigid diatomic ideal gas with volume $V$ at temperature $500 K$ undergoes an isobaric expansion to volume $3 V$. Assume $R=8.0 Jmol ^1 K^{-1}$. ($Q$) $7 kJ$

($III$) On mole of a monatomic ideal gas is compressed adiabatically from volume $V=\frac{1}{3} m^3$ and pressure $2 kPa$ to volume $\frac{v}{8}$ ($R$) $4 kJ$

($IV$) Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 kJ$ of heat and undergoes isobaric expansion. ($S$) $5 kJ$

($T$) $3 kJ$

Which one of the following options is correct?

Q: $List I$ describes thermodynamic processes in four different systems. $List II$ gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process. $List-I$ $List-II$ ($I$) $10^{-3} kg$ of water at $100^{\circ} C$ is converted to steam at the same temperature, at a pressure of $10^5 Pa$. The volume of the system changes from $10^{-6} m ^3$ to $10^{-3} m ^3$ in the process. Latent heat of water $=2250 kJ / kg$. ($P$) $2 kJ$ ($II$) $0.2$ moles of a rigid diatomic ideal gas with volume $V$ at temperature $500 K$ undergoes an isobaric expansion to volume $3 V$. Assume $R=8.0 Jmol ^1 K^{-1}$. ($Q$) $7 kJ$ ($III$) On mole of a monatomic ideal gas is compressed adiabatically from volume $V=\frac{1}{3} m^3$ and pressure $2 kPa$ to volume $\frac{v}{8}$ ($R$) $4 kJ$ ($IV$) Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 kJ$ of heat and undergoes isobaric expansion. ($S$) $5 kJ$ ($T$) $3 kJ$ Which one of the following options is correct?

c $(I)\Delta U =\Delta Q -\Delta W$ $=\left\{\left(10^{-3} \times 2250\right)-\frac{10^5\left(10^{-1}-10^{-4}\right)}{10^5}\right\} VJ$ $=(2.25-0.0999) VJ$ $=(2.1501) kJ$ $(II)$ $\Delta U = nC \Delta T$ $=\frac{5}{2} \pi R_{ T }$ $=\frac{5}{2} \cdot(0.2)(8)(1500-500) J$ $=4 kJ$ $(III)$ $P_1 V_2=P_2 V_2^2$ $\Rightarrow 2\left(\frac{1}{3}\right)^{s, 1}=P_2\left(\frac{1}{24}\right)^s$ $\Rightarrow P_2=64 kPa$ $\Delta U=n C_2 \Delta T=\frac{3}{2} \cdot\left(P_2 V_2-P_1 V_1\right)$ $=\frac{3}{2}\left(64 \times \frac{1}{24}-2 \times \frac{1}{3}\right) kJ$ $=3 VJ$ $(IV)\Delta U = HC C _{ V } \Delta T$ $= n \cdot \frac{7}{2} RAT$ $=\frac{7}{9} \Delta Q$ $=7 kJ$

Question

$List I$ describes thermodynamic processes in four different systems. $List II$ gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.

$List-I$	$List-II$
($I$) $10^{-3} kg$ of water at $100^{\circ} C$ is converted to steam at the same temperature, at a pressure of $10^5 Pa$. The volume of the system changes from $10^{-6} m ^3$ to $10^{-3} m ^3$ in the process. Latent heat of water $=2250 kJ / kg$.	($P$) $2 kJ$
($II$) $0.2$ moles of a rigid diatomic ideal gas with volume $V$ at temperature $500 K$ undergoes an isobaric expansion to volume $3 V$. Assume $R=8.0 Jmol ^1 K^{-1}$.	($Q$) $7 kJ$
($III$) On mole of a monatomic ideal gas is compressed adiabatically from volume $V=\frac{1}{3} m^3$ and pressure $2 kPa$ to volume $\frac{v}{8}$	($R$) $4 kJ$
($IV$) Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 kJ$ of heat and undergoes isobaric expansion.	($S$) $5 kJ$
	($T$) $3 kJ$

Which one of the following options is correct?

A$I \rightarrow T , II \rightarrow R , III \rightarrow S , IV \rightarrow Q$
B$I \rightarrow S , II \rightarrow P , III \rightarrow T , IV \rightarrow P$
C$I \rightarrow P, II \rightarrow R , III \rightarrow T , IV \rightarrow Q$
D$I \rightarrow Q , II \rightarrow R , III \rightarrow S , IV \rightarrow T$

IIT 2022, Advanced

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