Which of these statements are implied by the second law of thermodynamics?

The entropy of the Carnot engine operating in a cycle never decreases.
The increase in internal energy of a system in any process is the sum of heat absorbed plus work done on the system.
A heat engine, operating in a cycle, that rejects no heat to the low-temperature reservoir is impossible

Question

Which of these statements are implied by the second law of thermodynamics?

The entropy of the Carnot engine operating in a cycle never decreases.
The increase in internal energy of a system in any process is the sum of heat absorbed plus work done on the system.
A heat engine, operating in a cycle, that rejects no heat to the low-temperature reservoir is impossible

BlackTom AI · Accepted Answer

The question asks which statements are implied by the second law of thermodynamics, with three proposed items labeled A, B, and C.
Option A: The entropy of the Carnot engine operating in a cycle never decreases.
- Carnot engines are ideal reversible heat engines. For a complete cycle, the working substance returns to its initial state, so its entropy change over the cycle is zero. Saying the entropy never decreases aligns with the fact that, for a reversible cycle, the entropy change over the entire cycle is zero (it does not drop below its starting value and ends where it began).
- In more general terms, the second law does not require entropy to always increase in every part of a cycle for a reversible engine; it requires that the total change over a cycle is zero. Since a Carnot cycle is reversible, the net entropy change of the engine over the cycle is zero, which satisfies the idea that it does not decrease over the full cycle. This makes the statement plausible as a property of the Carnot cycle.
Option B: The increase in internal energy of a system in any process is the sum of heat absorbed plus work done on the system.
- This is a restatement of the first law of thermodynamics (ΔU = Q + W_on), not a direct implication of the second law. The second law concerns entropy changes and the directionality of processes, not the exact energy accounting relation. Therefore, while this equation is true under a common sign convention (where W_on is the work done on the system), it is not a consequence of the second law and may be considered outside the scope of what the second law asserts.
Option C: A heat engine, operating in a cycle, that rejects no heat to the low-temperature reservoir is impossible.
- This is a classic statement derived from the second law: in any real cyclic heat engine, some heat must be rejected to the cold reservoir; a cycle with no heat rejected to the cold reservoir would imply a perpetual motion machine of the second kind, which the second law forbids. Thus, this statement is directly implied by the second law.
In summary, evaluating each option: A aligns with the behavior of a reversible cycle like the Carnot cycle and its entropy changes over a full cycle; B is a first-law energy balance that is not a second-law consequence; C captures a second-law-imposed limitation on cyclic heat engines. The combination described by the question corresponds to the statements that are consistent with the second law.

SPHY001 Practice Quiz - Unit 15 | LA055

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