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  • Which of the following relations are correct? <img alt="(A)\, \, \Delta \mathrm{U}=\mathrm{q}+\mathrm{p} \Delta \mathrm{V}" src="https://entrancecorner.oncodecogs.com/gif.latex?%28A%29%5C

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{q_{\text {rev }}}{T}                     (D)\, \, \Delta \mathrm{H}=\Delta \mathrm{U}-\Delta \mathrm{nRT}

Choose the most appropriate answer from the options given below:

Option: 1

B and D Only


Option: 2

A and B Only


Option: 3

B and C Only


Option: 4

C and D Only


Answers (1)

best_answer

Only (B) and (C) are correct.
(B) \, \, \mathrm{G}=\mathrm{H}-\mathrm{TS}
At constant \mathrm{T}
$$ \Delta \mathrm{G}=\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S}
(A) First law is given by
$$ \Delta \mathrm{U}=\mathrm{Q}+\mathrm{W}
If we apply constant \mathrm{P} and reversible work.
$$ \Delta \mathrm{U}=\mathrm{Q}-\mathrm{P} \Delta \mathrm{V}
(C) By definition of entropy change
$$ \mathrm{dS}=\frac{\mathrm{q}_{\mathrm{rev}}}{\mathrm{T}}
At constant \mathrm{T}
$$ \Delta \mathrm{S}=\frac{\mathrm{q}_{\mathrm{rev}}}{\mathrm{T}}
(D) \, \, \mathrm{H}=\mathrm{U}+\mathrm{PV}
For ideal gas
\mathrm{H}=\mathrm{U}+\mathrm{nRT}
At constant T
\Delta \mathrm{H}=\Delta \mathrm{U}+\Delta \mathrm{nRT}

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