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Thermodynamics question

2023 · 29 Jan · Shift 2 · Q3
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Thermodynamics question

2023 · 29 Jan · Shift 2 · Q3

JEE MainChemistryThermodynamicsMCQ+4 / −1
Which of the following relations are correct? (A) ΔU=q+pΔV\mathrm{\Delta U=q+p\Delta V}ΔU=q+pΔV(B) ΔG=ΔH−TΔS\mathrm{\Delta G=\Delta H-T\Delta S}ΔG=ΔH−TΔS(C) ΔS=qrevT\Delta \mathrm{S}=\frac{q_{rev}}{T}ΔS=Tqrev​​(D) ΔH=ΔU−ΔnRT\mathrm{\Delta H=\Delta U-\Delta nRT}ΔH=ΔU−ΔnRT Choose the most appropriate answer from the options given below :
  1. A
    A and B only
  2. B
    B and C only
  3. C
    C and D only
  4. D
    B and D only
View written solutionFree

Correct answer: B

  1. We check each relation one by one.
  1. Statement (A): ΔU=q+pΔV\Delta U = q + p\Delta VΔU=q+pΔV

From the first law of thermodynamics,

ΔU=q+w\Delta U = q + wΔU=q+w

If only pressure-volume work is done against constant external pressure,

w=−pΔVw = -p\Delta Vw=−pΔV

So,

ΔU=q−pΔV\Delta U = q - p\Delta VΔU=q−pΔV

not q+pΔVq + p\Delta Vq+pΔV.

So, (A) is incorrect.

  1. Statement (B): ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta SΔG=ΔH−TΔS

By definition of Gibbs free energy,

G=H−TSG = H - TSG=H−TS

Hence for a process at constant temperature,

ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta SΔG=ΔH−TΔS

So, (B) is correct.

  1. Statement (C): ΔS=qrevT\Delta S = \dfrac{q_{\text{rev}}}{T}ΔS=Tqrev​​

Entropy change is defined for a reversible process as

ΔS=∫δqrevT\Delta S = \int \frac{\delta q_{\text{rev}}}{T}ΔS=∫Tδqrev​​

If temperature is constant, this becomes

ΔS=qrevT\Delta S = \frac{q_{\text{rev}}}{T}ΔS=Tqrev​​

This is the standard relation used in thermodynamics for reversible isothermal change.

So, (C) is correct.

  1. Statement (D): ΔH=ΔU−ΔnRT\Delta H = \Delta U - \Delta nRTΔH=ΔU−ΔnRT

We know,

H=U+PVH = U + PVH=U+PV

For ideal gases,

PV=nRTPV = nRTPV=nRT

Therefore,

ΔH=ΔU+ΔngRT\Delta H = \Delta U + \Delta n_g RTΔH=ΔU+Δng​RT

(at constant temperature, for gaseous moles change).

So the sign should be plus, not minus. Hence (D) is incorrect.

  1. Therefore, the correct statements are:
(B) and (C)(B) \text{ and } (C)(B) and (C)

So the correct option is Option B.

  1. Comparison with stored answer

Stored correct answer: B
Derived answer: B

They match.

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