Question

Which is true for a cyclic process?

• A. \( \Delta E = 0 \)
• B. \( \Delta E = q - W \)
• C. \( q = W \)
• D. All of these

Hint:

Cyclic process $\Rightarrow$ initial state = final state $\Rightarrow$ \(\Delta E = 0\).

Answer 1

The Correct Option is A

A cyclic process is a thermodynamic process that returns a system to its initial state at the end of the process. This means that the internal energy of the system, \( E \), at the end of the process is the same as at the beginning.

The change in internal energy \( \Delta E \) is given by the formula:

\( \Delta E = E_{\text{final}} - E_{\text{initial}} \)

Since the initial and final states are the same in a cyclic process, we have:

\( \Delta E = 0 \)

This is the defining characteristic of a cyclic process; the internal energy does not change over the complete cycle.

Let's consider the other options:

• \Delta E = q - W is the first law of thermodynamics where \( q \) is the heat added to the system and \( W \) is the work done by the system. While this equation is true in general, it simplifies to \( \Delta E = 0 \) for a cyclic process.
• q = W implies that the heat added to the system is equal to the work done by the system. This is a special condition that can occur in certain types of cyclic processes, like in Carnot cycles, but it is not generally true for all cyclic processes.
• "All of these" is not correct because not every cyclic process will have \( q = W \).

Therefore, the correct answer is: \( \Delta E = 0 \). This aligns with the fundamental nature of cyclic processes where the internal energy remains unchanged over a complete cycle.