Matching List : List - I List - II (P) n moles of ideal gas undergoes adiabatic irreversible expansion from temperature T 1 to T 2 and volume V 1 to V 2 (1) Δ S surrounding

Question

Matching List : List - I List - II (P) n moles of ideal gas undergoes adiabatic irreversible expansion from temperature T 1 ​ to T 2 ​ and volume V 1 ​ to V 2 ​ (1) Δ S surrounding ​ < 0 (Q) n moles of ideal gas undergoing reversible expansion from temperature T 1 ​ to T 2 ​ and volume V 1 ​ to V 2 ​ (nonadiabatic) (2) Δ S system ​ = nC V , m ​ ln ( T 1 ​ T 2 ​ ​ ) + nR ln ( V 1 ​ V 2 ​ ​ )  = 0 (R) n moles of ice at 0 ∘ C ( T 1 ​ ) change to water vapour at 10 0 ∘ C ( T 2 ​ ) at 1 bar (3) (S) ′ n ′ moles of liquid benzene at 2 5 ∘ C ( T 1 ​ ) changes to benzene vapours at 7 8 ∘ C ( T 2 ​ ) [where boiling point of benzene = 7 8 ∘ C ] at 1 bar (4) Δ S surrounding ​ = 0 (5) Select the incorrect option :

TestHub · Accepted Answer

Question Explanation: The objective is to match various thermodynamic processes (List-I) with their specific entropy or work expressions (List-II).

Concept:

This question is based on the calculation of various thermodynamic processes.

Solution:

(P) Initial state ( $V_{1}$ , $T_{1}$ ) to final state ( $V_{2}$ , $T_{2}$ ), entropy change for an ideal gas:

$Δ S_{sys t e m} = n C_{v} ln (\frac{T _{2}}{T _{1}}) + n R ln (\frac{V _{2}}{V _{1}}) \neq = 0$

$Δ S_{s u rro u n d in g} = \frac{q _{s u rro u n d in g}}{T _{s u rro u n d in g}} = 0 (q_{s u rro u n d in g} = 0)$

Since the process is adiabatic:

$w = n C_{v} (T_{2} - T_{1})$

$w = \frac{n R}{γ - 1} (T_{2} - T_{1})$

(Q) Initial state ( $V_{1}$ , $T_{1}$ ) to final state ( $V_{2}$ , $T_{2}$ ):

$Δ S_{sys t e m} = n C_{v} ln (\frac{T _{2}}{T _{1}}) + n R ln (\frac{V _{2}}{V _{1}}) \neq = 0$

Since the process is reversible:

$Δ S_{u ni v erse} = 0 = Δ S_{sys t e m} + Δ S_{s u rro u n d in g}$

$Δ S_{s u rro u n d in g} = - Δ S_{sys t e m}$

List - I	List - II
(P) n moles of ideal gas undergoes adiabatic irreversible expansion from temperature $T_{1}$ to $T_{2}$ and volume $V_{1}$ to $V_{2}$	(1) $Δ S_{surrounding} < 0$
(Q) n moles of ideal gas undergoing reversible expansion from temperature $T_{1}$ to $T_{2}$ and volume $V_{1}$ to $V_{2}$ (nonadiabatic)	(2) $Δ S_{system} = nC_{V, m} ln (\frac{T _{2}}{T _{1}}) + nR ln (\frac{V _{2}}{V _{1}}) \neq = 0$
(R) n moles of ice at $0^{\circ} C (T_{1})$ change to water vapour at $10 0^{\circ} C (T_{2})$ at 1 bar	(3)
(S) $^{'} n^{'}$ moles of liquid benzene at $2 5^{\circ} C (T_{1})$ changes to benzene vapours at $7 8^{\circ} C (T_{2})$ [where boiling point of benzene $= 7 8^{\circ} C$ ] at 1 bar	(4) $Δ S_{surrounding} = 0$
	(5)

Chemistry - Thermodynamics - II Question with Solution | TestHub

Options:

Doubts & Discussion