\(A\) અને \(B\) બે ગૅસ માટે ગ્રાફ આપેલ છે.જ્યાં \(\Delta Q_A\) અને \(\Delta Q_B\) તંત્ર દ્વારા શોષાતી ઉષ્મા અને \(\Delta U_A\) અને \(\Delta U_B\) આંતરિક ઉષ્મામાં થતો ફેરફાર હોય તો નીચેનામાથી શું સાચું થાય?

A \(\Delta {Q_A}\, = \,\Delta {Q_B}\,;\,\Delta {U_A} = \Delta {U_B}\)
B \(\Delta {Q_A}\, > \,\Delta {Q_B}\,;\,\Delta {U_A} = \Delta {U_B}\)
C \(\Delta {Q_A}\, < \,\Delta {Q_B}\,;\,\Delta {U_A} < \Delta {U_B}\)
D \(\Delta {Q_A}\, > \,\Delta {Q_B}\,;\,\Delta {U_A} > \Delta {U_B}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\Delta {Q_A}\, > \,\Delta {Q_B}\,;\,\Delta {U_A} = \Delta {U_B}\)

Step-by-step Solution

Detailed explanation

Initial and final states for both the processes are same, \(\therefore \Delta \mathrm{U}_{\mathrm{A}}=\Delta \mathrm{U}_{\mathrm{B}}\) Work done during process \(A\) is greater than in process \(B\). Because area is more By First law of thermodynamics \(\Delta Q=\Delta U+W\)…

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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