Which of the following relations are correct? (A) \(\Delta \mathrm{U}=\mathrm{q}+\mathrm{p} \Delta \mathrm{V}\) (B) \(\Delta \mathrm{G}=\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S}\) (C) \(\Delta \mathrm{S}=\frac{\mathrm{q}_{\text {rev }}}{\mathrm{T}}\) (D) \(\Delta \mathrm{H}=\Delta \mathrm{U}-\Delta \mathrm{nRT}\) Choose the most appropriate answer from the options given below :

JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Chemical Thermodynamics

Which of the following relations are correct?
(A)

Δ U = q + p Δ V

(B)

Δ G = Δ H - T Δ S

(C)

Δ S = \frac{q _{rev}}{T}

(D)

Δ H = Δ U - Δ nRT

Choose the most appropriate answer from the options given below :

Answer: (B)

The first law states that the change in internal energy is the sum of the heat absorbed and the work done on the system, and for pressure

-

volume work during expansion this work is

- p Δ V

, so

Δ U = q - p Δ V

rather than

q + p Δ V

. The Gibbs energy change at constant temperature is defined by

Δ G = Δ H - T Δ S

, which is a correct relation. The entropy change for a reversible change at constant temperature is

Δ S = \frac{q _{rev}}{T}

, also correct. Relating enthalpy and internal energy for a gaseous reaction gives

Δ H = Δ U + Δ n_{g} R T

, so the form carrying a minus sign is wrong. The relations that hold are

Δ G = Δ H - T Δ S

and

Δ S = \frac{q _{rev}}{T}

JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Single correct option