A gas undergoes a change at constant temperature. Which of the following quantities remain fixed ?

Options

A. Pressure
B. Entropy
C. Heat exchanged with the system
D. All the above may change

Answer

To solve the question regarding which quantities remain fixed when a gas undergoes a change at constant temperature, we can analyze each option step by step.

### Step 1: Understand the Ideal Gas Law
The ideal gas law is given by the equation:
\[ PV = nRT \]
Where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles of gas (constant)
- \( R \) = ideal gas constant (constant)
- \( T \) = temperature (constant in this case)

### Step 2: Analyze the First Option - Pressure
Since the temperature \( T \) is constant, we can rearrange the ideal gas law to:
\[ PV = \text{constant} \]
This implies that if the volume \( V \) changes, the pressure \( P \) must also change to keep the product \( PV \) constant. Therefore, pressure does not remain fixed.

**Hint:** Remember that in an isothermal process (constant temperature), if one variable changes, the other must adjust to maintain the relationship defined by the ideal gas law.

### Step 3: Analyze the Second Option - Entropy
Entropy change \( \Delta S \) is defined as:
\[ \Delta S = \int \frac{dQ_{\text{rev}}}{T} \]
Since \( T \) is constant, we can factor it out:
\[ \Delta S = \frac{1}{T} \int dQ_{\text{rev}} \]
This means that the change in entropy depends on the heat exchanged \( Q \). If \( Q \) changes, then \( \Delta S \) will also change. Therefore, entropy does not remain fixed.

**Hint:** Entropy is a measure of disorder or energy dispersal, and it changes with heat transfer, especially in processes where temperature is constant.

### Step 4: Analyze the Third Option - Heat Exchange (Q)
From the first law of thermodynamics, we have:
\[ Q = \Delta U + W \]
In an isothermal process for an ideal gas, the change in internal energy \( \Delta U \) is zero (since internal energy depends only on temperature). Thus:
\[ Q = W \]
Since work \( W \) can vary during an isothermal process (depending on how the gas expands or compresses), \( Q \) will also vary. Therefore, heat exchange does not remain fixed.

**Hint:** The first law of thermodynamics shows that heat exchange is directly related to work done and internal energy changes, which can vary in an isothermal process.

### Step 5: Conclusion
After analyzing all options:
- Pressure does not remain fixed.
- Entropy does not remain fixed.
- Heat exchange does not remain fixed.

Thus, the correct answer is:
**All of the above may change.**

**Final Answer: Option D - All of the above may change.**