Second Law – Choose the Correct Formal Statements Select the correct formulation(s) of the second law of thermodynamics. The Kelvin–Planck engine statement and the Clausius heat-pump statement are both valid and equivalent expressions.
-
AIt is impossible to construct an engine working on a cyclic process, whose sole purpose is to convert heat energy into work.
-
BIt is impossible to transfer heat from a body at a lower temperature to a higher temperature, without the aid of an external source.
-
CThere is a definite amount of mechanical energy obtainable from any given amount of heat energy.
-
DBoth (a) and (b) are correct second-law statements.
-
EAll of the above are correct.
Answer
Correct Answer: Both (a) and (b) are correct second-law statements.
Explanation
Introduction / Context:The second law can be stated in multiple, equivalent ways. Two classical forms are the Kelvin–Planck statement (about the impossibility of 100% heat-to-work conversion in a cyclic engine) and the Clausius statement (about the impossibility of heat flowing spontaneously from cold to hot without external aid).
Given Data / Assumptions:
- Cyclic devices interacting with thermal reservoirs.
- Macroscopic classical thermodynamics; no statistical exceptions considered.
- Standard sign conventions for heat and work.
Concept / Approach:
Statement (a) is the Kelvin–Planck form: no engine can completely convert heat from a single reservoir to work. Statement (b) is the Clausius form: heat cannot, of itself, flow from colder to hotter bodies. These two are logically equivalent; violating one enables violation of the other. Statement (c) is not a correct second-law statement; it resembles an inaccurate interpretation of the mechanical equivalent of heat and ignores the second-law efficiency limits.
Step-by-Step Solution:
Evaluate (a): matches Kelvin–Planck → valid.Evaluate (b): matches Clausius → valid.Evaluate (c): incorrect; the second law does not guarantee a definite full conversion of heat to work.Therefore, choose the option asserting both (a) and (b) are correct.Verification / Alternative check:
Textbook proofs show that a hypothetical device violating Kelvin–Planck can be used to construct a device violating Clausius, and vice versa, establishing equivalence.
Why Other Options Are Wrong:
Option (e) includes (c), which is false. Picking only (a) or only (b) ignores the presence of the other correct statement.
Common Pitfalls:
Confusing first-law energy conversion statements with second-law limitations; assuming (c) is a conservation statement when it actually misstates second-law restrictions.
Final Answer:
Both (a) and (b) are correct second-law statements.