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° C is converted to steam at the same temperature, at a pressure of 105 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=(1/3) m 3 and pressure 2 kPa to volume (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?

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° C is converted to steam at the same temperature, at a pressure of 105 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=(1/3) m 3 and pressure 2 kPa to volume (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 arrow T, II arrow R, III arrow S, IV arrow Q (B) I arrow S, II arrow P, III arrow T, IV arrow P (C) I arrow P, II arrow R, III arrow T, IV arrow Q (D) I arrow Q, II arrow R, III arrow S, IV arrow T

Tardigrade Admin · Accepted Answer

(I) Δ U =Δ Q -Δ W = (10-3 × 2250)-(105(10-3-10-6)/103) kJ =(2.25-0.0999) kJ =(2.1501) kJ (II) Δ U = nC V Δ T =(5/2) nR Δ T =(5/2) ⋅(0.2)(8)(1500-500) J =4 kJ (III) P1 V2&gamma;=P2 V2&gamma; ⇒ 2((1/3))5 / 3=P2((1/24))5 / 3 ⇒ P2=64 k Pa Δ U=n v Δ T =(3/2) ⋅( P 2 V 2- P 1 V 1) =(3/2)(64 × (1/24)-2 × (1/3)) kJ =3 kJ (IV) Δ U = nC V Δ T = n ⋅ (7/2) R Δ T =(7/9) Δ Q =7 kJ

I $\to$ T, II $\to$ R, III $\to$ S, IV $\to$ Q

I $\to$ S, II $\to$ P, III $\to$ T, IV $\to$ P

I $\to$ P, II $\to$ R, III $\to$ T, IV $\to$ Q

I $\to$ Q, II $\to$ R, III $\to$ S, IV $\to$ T

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 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 $R = 8.0 J m o l^{- 1} K^{- 1}$ .	Q	7 KJ
III	On mole of a monatomic ideal gas is compressed adiabatically from volume $V = \frac{1}{3} m^{3}$ and pressure $2 k P a$ to volume $\frac{v}{8}$	R	4 KJ
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 KJ
		T	3 KJ

I → T, II → R, III → S, IV → Q

I → S, II → P, III → T, IV → P

I → P, II → R, III → T, IV → Q

I → Q, II → R, III → S, IV → T

I $\to$ T, II $\to$ R, III $\to$ S, IV $\to$ Q

I $\to$ S, II $\to$ P, III $\to$ T, IV $\to$ P

I $\to$ P, II $\to$ R, III $\to$ T, IV $\to$ Q

I $\to$ Q, II $\to$ R, III $\to$ S, IV $\to$ T