If one complete cycle of a reversible process is carried out on a sample of an ideal so that its final state is the same as its initial state , which one of the following quantities is the only one which can be non - zero ?

Options

A. The change in volume of the sample
B. the net heat absorbed by the sample
C. the change in the entropy of the example
D. the change in temperature of the sample

Answer

To solve the problem, we need to analyze the situation of a reversible process carried out on an ideal gas in a cyclic manner. Here’s the step-by-step solution:

### Step 1: Understand the Concept of a Reversible Process
A reversible process is one where the system can be returned to its initial state without leaving any change in the surroundings. This means that the path taken during the process can be reversed, and the system will follow the same path in the opposite direction.

**Hint:** Remember that in a reversible process, the system and surroundings can be returned to their original states without any net changes.

### Step 2: Understand the Concept of a Cyclic Process
In a cyclic process, the initial and final states of the system are the same. This implies that any state function (like internal energy, temperature, pressure, etc.) will have no net change over one complete cycle.

**Hint:** A cyclic process means that all state functions return to their original values after the cycle is completed.

### Step 3: Identify State Functions vs. Path Functions
State functions are properties that depend only on the state of the system and not on how it got there. Examples include internal energy (U), temperature (T), pressure (P), and entropy (S). In contrast, heat (Q) and work (W) are path functions, meaning they depend on the specific process taken.

**Hint:** State functions are independent of the path taken, while path functions depend on the specific process.

### Step 4: Analyze Changes in State Functions During a Cycle
Since the process is cyclic, we can conclude that:
- Change in internal energy (ΔU) = 0
- Change in temperature (ΔT) = 0
- Change in pressure (ΔP) = 0
- Change in entropy (ΔS) = 0
- Change in enthalpy (ΔH) = 0

**Hint:** For any state function in a cyclic process, the change is zero because the initial and final states are the same.

### Step 5: Analyze Heat Transfer in a Reversible Cycle
In a reversible process, the heat absorbed by the system during one direction of the process will be equal in magnitude but opposite in sign to the heat released during the reverse process. Therefore, the net heat transfer over one complete cycle is also zero.

**Hint:** In a reversible cycle, the heat absorbed and released cancels out, leading to a net heat change of zero.

### Step 6: Conclusion
Given that all state functions have a change of zero in a cyclic process, and since heat is a path function that can vary, the only quantity that can be non-zero in this scenario is the work done (W) during the process, because it can vary depending on the path taken, even though the net change in energy is zero.

**Final Answer:** The only quantity that can be non-zero is the **work done (W)** during the process.