Two systems X and Y are in thermal equilibrium. If X is heated at constant volume and Y is heated at constant pressure, and again finally maintained at thermal equilibrium, then heat Q given to the system X and Y and internal energy U stored in the systems X and Y are:
Correct answer: D. Qx < Qy and Ux = Uy
- A. Qx = Qy and Ux = Uy
- B. Qx = Qy and Ux < Uy
- C. Qx < Qy and Ux < Uy
- D. Qx < Qy and Ux = Uy
Explanation
When heating occurs at constant volume, all the heat added increases the internal energy, whereas at constant pressure, some heat contributes to doing work (expanding the system). Therefore, Qy > Qx. However, since both systems are in thermal equilibrium before and after, their internal energy changes, Ux and Uy, are equal. Thus, the correct answer is that Qx < Qy and Ux = Uy. This explains why option D is correct, while options A, B, and C are incorrect.
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About First Law of Thermodynamics
The first law relates heat supplied, work done and the change in internal energy through energy conservation. Problems use sign conventions and apply the law to isothermal, adiabatic, isobaric and isochoric processes. Internal energy is a state function, while heat and work depend on the path followed.
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