એક પ્રવાહીને જ્યારે \(25^{\circ} \mathrm{C}\) તાપમાને ઉષ્મા-અવરોધક બંધ પાત્રમાં રાખવામાં આવ્યું હતું ત્યારે તેને બહારથી યાંત્રિક રીતે હલાવવામાં આવ્યું. નીચેના ઉષ્માગતિશીલ પ્રાચલો માટે કયો સાચો વિકલ્પ હશે?

A \(\Delta \mathrm{U} \lt 0, \mathrm{q}=0, \mathrm{w}\gt0\)
B \(\Delta \mathrm{U}=0, \mathrm{q}=0, \mathrm{w}=0\)
C \(\Delta \mathrm{U}\gt0, \mathrm{q}=0, \mathrm{w}\gt0\)
D \(\Delta \mathrm{U}=0, \mathrm{q} \lt 0, \mathrm{w}\gt0\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\Delta \mathrm{U}\gt0, \mathrm{q}=0, \mathrm{w}\gt0\)

Step-by-step Solution

Detailed explanation

ઉષ્મા-અવરોધક \(\Rightarrow q=0\) ઉષ્માગતિશાસ્ત્રના પ્રથમ નિયમ અનુસાર \(\begin{aligned} & \Delta \mathrm{U}=\mathrm{q}+\mathrm{w} \\ & \Delta \mathrm{U}=\mathrm{w} \\ & \mathrm{w}>0, \Delta \mathrm{U}>0 \end{aligned}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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