Second Law and Entropy Analysis Questions and Answers

Answer: C

Correct answer: a reversible isothermal expansion

Reversibility is by definition the absence of entropy generation: the system’s entropy rises but the reservoir’s falls by exactly as much, so the total is unchanged. The other three are the standard irreversibilities - mixing, heat flow across a finite temperature difference, and friction - and each of them produces entropy that nothing can recover.

Answer: D

Correct answer: 50 degrees Celsius

Equal masses of the same substance with the same specific heat meet in the middle: \[ \frac{100+0}{2} = 50\ \mathrm{degrees}. \] The energy balance is symmetric, so no heat capacity value is needed. The process is spontaneous and irreversible, and although energy is conserved the entropy of the two streams together increases - which is why the mixing cannot be undone without work.

Answer: A

The energy balance is satisfied exactly, yet the capacity of that energy to do work has fallen because the temperature difference has been destroyed. This is the clearest illustration of what the second law adds to the first.

Answer: B

Streams carry entropy in and out, heat transfer carries entropy across the boundary, and irreversibility adds the generation term. At steady state the inventory inside does not change, which is what allows the balance to be written this way.

Answer: C

Correct answer: the extra work a reversible process would have delivered

Lost work is the shortfall against the reversible ideal - the work a perfect process would have produced and this one did not, or the extra work this one consumed. It is not the same as the heat dissipated internally, though friction contributes to it, and it is the quantity a second-law analysis exists to locate.

Answer: D

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason names the constant. The Gouy-Stodola relation is \[ W_{lost} = T_0 S_{gen}, \] where \( T_0 \) is the temperature of the surroundings. It is what makes entropy generation an engineering quantity rather than an abstraction: multiply it by the ambient temperature and the answer is in watts, so the components of a plant can be ranked by the work each one wastes.

Answer: A

Correct answer: the dead state in equilibrium with the surroundings

Exergy is the maximum useful work obtainable as a stream is brought to equilibrium with its environment, so it is measured against that environment - the dead state, at the pressure and temperature of the surroundings. A stream at ambient conditions has no exergy however much energy it contains, which is exactly the distinction between the two quantities.

Answer: B

The first two are correct and define how exergy is used. The third confuses exergy with energy, since the whole value of an exergy analysis lies in the fact that it is not conserved. Where it disappears is where the plant is losing money.

Answer: C

Conservation of energy is the first law and says nothing about direction. The distinction matters because a proposed device can satisfy the first law perfectly and still be impossible. Perpetual motion of the second kind is exactly such a device.

Answer: D

Work is used to move heat rather than to create it, so several units of heat can be pumped per unit of work. Calling it an efficiency invites the mistaken objection that it exceeds unity. Values between two and five are usual for domestic machines.