A closed system undergoes a cycle consisting of two processes. Process 1 - 2 is an isothermal expansion whereas Process 2 - 1 is an isentropic compression. According to the first law of thermodynamics, which of the following statements is true for this cycle?

Concept:

In thermodynamic cycles, the first law of thermodynamics (energy conservation) states that the net work done by the system over one complete cycle is equal to the net heat added to the system. Let's analyze each process in the given cycle and determine the correctness of the statements.

Process 1 - 2: Isothermal Expansion

• Isothermal Process: During an isothermal process, the temperature remains constant.
• First Law of Thermodynamics: \(Q_{1-2} = W_{1-2}\)
• Since the internal energy change ( \(\Delta U\) ) for an isothermal process of an ideal gas is zero (as \(\Delta T = 0\) ), the heat transfer ( \(Q_{1-2}\) ) is equal to the work done ( \(W_{1-2}\) ).
• Therefore, heat transfer during Process 1 - 2 is not zero. Also, work done during Process 1 - 2 is not zero.

Process 2 - 1: Isentropic Compression

• Isentropic Process: During an isentropic process, the entropy remains constant, and the process is adiabatic (no heat transfer).
• First Law of Thermodynamics: \(Q_{2-1}\) = 0
• For an isentropic process, the heat transfer ( \(Q_{2-1}\) ) is zero. However, there is work done during this process ( \(W_{2-1}\) ) since the system is being compressed.
• Therefore, heat transfer during Process 2 - 1 is zero, but work done during Process 2 - 1 is not zero.

Conclusion

Based on the analysis of the processes:2) Heat transfer during Process 2 - 1 is zero.