અચળ દબાણ \(100\, N/m^2\) એ વાયુનું કદ \(2\,m^3\) થી \(1\,m^3\) થાય છે.પછી તેને અચળ કદે ગરમ કરવા \(150\, J\) ઉષ્મા આપવામાં આવે છે. વાયુની આંતરિક ઉર્જામાં કેટલો ફેરફાર થાય?

A \(250\, J\) વધે
B \(250\, J\) ઘટે
C \(50\, J\) વધે
D \(50\, J\) ઘટે

Verified Solution

Answer & Solution

Correct Answer

(A) \(250\, J\) વધે

Step-by-step Solution

Detailed explanation

As we know, \(\Delta Q=\Delta u+\Delta w\) (Ist law of thermodynamics) \(\Rightarrow \Delta \mathrm{Q}=\Delta \mathrm{u}+\mathrm{P} \Delta \mathrm{v}\) or \(150=\Delta u+100(1-2)\) \(=\Delta u-100\) \(\therefore \Delta u=150+100=250 \mathrm{J}\) Thus the internal energy of the…

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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