Consider an isentropic compression of air in a closed system. Which of the following statements are correct?

Question

BlackTom AI · Accepted Answer

Isentropic for a closed system means the process is reversible and adiabatic: Q = 0 (no heat transfer) and no mass crosses the boundary. The relevant fundamental relation is the first law for a closed system: ΔE = Q - W. With negligible kinetic and potential energy changes, ΔE = ΔU (internal energy change).

Step-by-step reasoning and algebra:
1. Start with the first law for a closed system: ΔU = Q - W, where W is the work done by the system (standard sign convention).
2. For an isentropic (adiabatic, reversible) process: Q = 0.
3. Substitute Q = 0: ΔU = -W.
4. Rearranging gives W = -ΔU.

Interpretation of signs:
- W here is work done by the system. For compression work done on the system, W (by the system) is negative and ΔU is positive, consistent with ΔU = -W.
- If someone uses W_on to mean work done on the system, then W_on = -W = ΔU (i.e., work done on the system equals the increase in internal energy).

Why option c is correct:
Option c states “The work done is equal to the change in internal energy (times (-1)).” This matches W = -ΔU (work by the system equals minus the internal energy change) derived above, so option c is correct.

Why the other options are incorrect:
a) “The work done is equal to the heat transfer.” With Q = 0 but W ≠ 0 for compression, this is false.  
b) “The heat transfer is equal to the change in internal energy.” That would require W = 0; not true for compression.  
d) “No work is done.” False — compression implies boundary work is done.  
e) “The heat transfer is equal to the change in enthalpy.” Enthalpy relations apply to open/flow problems at constant pressure; for closed-system adiabatic compression, Q = 0 and ΔH is not the relevant equality.

Conclusion: The correct statement is option c, which matches W = -ΔU as shown above.

Consider an isentropic compression of air in a closed system. Which of the following statements are correct?单项选择题

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