Which statements about thermodynamic processes and heat engines is/are correct? 1. Work done in irreversible expansion is greater than in quasi-static expansion. 2. Efficiency of an ideal heat engine depends only on reservoir temperatures. 3. Heat flows from cold to hot only with external work.
- (a)1 and 2 only
- (b)2 and 3 only
- (c)1 and 3 only
- (d)1, 2 and 3
Answer
Why
Correct — B. Test each statement.
Statement 1 is false. For the same isothermal expansion, the quasi-static (reversible) path delivers the most work. An irreversible expansion pushes against a smaller opposing pressure and does less.
Statement 2 is true. An ideal (Carnot) engine has efficiency η = 1 − T₂⁄T₁, fixed by the reservoir temperatures in kelvin.
Statement 3 is true. This is the Clausius statement: heat goes from cold to hot only when external work is done, as in a refrigerator.
2 and 3 only → option (b).
Why the others are wrong
- (a)1 and 2 only — It keeps statement 1, which reverses the rule: the quasi-static path does the most work. It also drops statement 3, the Clausius statement.
- (c)1 and 3 only — It keeps statement 1, which is false: irreversible expansion does less work than quasi-static. It also drops statement 2, the Carnot result.
- (d)1, 2 and 3 — Statement 1 is false, so all three cannot stand. Free expansion into a vacuum is the extreme case: it is irreversible and does no work at all.
Concept
A quasi-static process runs so slowly that the system stays in equilibrium with its surroundings at every stage. Without friction or other losses, it is reversible.
The second law limits engines. By Carnot's theorem, no engine working between two temperatures is more efficient than a reversible engine between them, and that efficiency, 1 − T₂⁄T₁, does not depend on the working substance.
In Clausius's form, the law forbids any process whose sole result is heat passing from a colder body to a hotter one.
Use kelvin in η = 1 − T₂⁄T₁. An engine between 27 °C and 127 °C works between 300 K and 400 K, so η = 1 − 300⁄400 = 25%. Celsius values would give about 79%, which is wrong.
Key facts
- Carnot (ideal reversible) engine efficiency: η = 1 − T₂⁄T₁, with both temperatures in kelvin.
- The efficiency of a reversible engine does not depend on the working substance.
- Clausius statement: no process can have as its sole result the transfer of heat from a colder body to a hotter one.
- For the same isothermal expansion, the reversible path does the most work, and free expansion does none.
Study next
Common traps
- Assuming a fast, violent expansion does more work: the work is set by the opposing pressure, which is lower in an irreversible expansion.
- Putting Celsius temperatures into η = 1 − T₂⁄T₁: the formula needs kelvin.
Here three textbook claims are checked one by one, and the false one reverses a comparison. Heat physics also appears at 15 Sep 2025, 09:00, GA Q.17, which keys latent heat of vaporisation for why steam at 100°C burns worse than boiling water.
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