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 $R=8.0 J mol^{-1} K^{-1}$. | (Q) | $7 kJ$ | | (III) | One 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→T, II→R, III→S, IV→Q

(B) I→S, II→P, III→T, IV→P

(D) I→Q, II→R, III→S, IV→T

Heat & Thermodynamics — JEE Advanced · 2022 · 28 Aug 2022 · Paper 1 Question with Solution

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)	$1 0^{- 3} k g$ of water at $10 0^{\circ} C$ is converted to steam at the same temperature, at a pressure of $1 0^{5} P a$ . The volume of the system changes from $1 0^{- 6} m^{3}$ to $1 0^{- 3} m^{3}$ in the process. Latent heat of water $= 2250 k J / k g$ .	(P)	$2 k J$
(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 $R = 8.0 J m o l^{- 1} K^{- 1}$ .	(Q)	$7 k J$
(III)	One mole of a monatomic ideal gas is compressed adiabatically from volume $V = \frac{1}{3} m^{3}$ and pressure $2 k P a$ to volume $\frac{V}{8}$ .	(R)	$4 k J$
(IV)	Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 k J$ of heat and undergoes isobaric expansion.	(S)	$5 k J$
		(T)	$3 k J$

Which one of the following options is correct?

(A)I→T, II→R, III→S, IV→Q
(B)I→S, II→P, III→T, IV→P
(C)I→P, II→R, III→T, IV→Q✓ Correct
(D)I→Q, II→R, III→S, IV→T

Answer: (C)

Solution

(I)

Δ U = Δ Q - Δ W = (1 0^{- 3} \times 2250 \times 1 0^{3}) - (1 0^{5} \times (1 0^{- 3} - 1 0^{- 6}))

= 2250 - 99.9 \approx 2150 J \approx 2 k J

I→P

(II) Isobaric expansion of diatomic gas:

Δ U = n C_{V} Δ T = n \times \frac{5 R}{2} \times Δ T

From

V_{1} / T_{1} = V_{2} / T_{2}

T_{2} = 1500 K

, so

Δ T = 1000 K

Δ U = 0.2 \times \frac{5 \times 8}{2} \times 1000 = 4000 J = 4 k J

II→R

(III) Adiabatic compression of monatomic gas (

γ = 5/3

P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ} \Rightarrow P_{2} = 2 \times 8^{5/3} = 64 k P a

Δ U = \frac{3}{2} (P_{2} V_{2} - P_{1} V_{1}) = \frac{3}{2} (64 \times \frac{1}{24} - 2 \times \frac{1}{3}) = 3 k J

III→T

(IV) Diatomic gas with vibration (

C_{V} = 7 R /2

Δ U = n C_{V} Δ T = \frac{7}{9} Δ Q = \frac{7}{9} \times 9 = 7 k J

IV→Q

Answer: (C) I→P, II→R, III→T, IV→Q

JEE Advanced · 2022 · 28 Aug 2022 · Paper 1 · Single correct option

JEE Advanced · 2022 · 28 Aug 2022 · Paper 1 · Heat & Thermodynamics

Solution

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