If a gas, at constant temperature and pressure expands, then its

Options

A. Entropy increases and then decreases
B. Internal enery increases
C. Internal energy remains the same
D. Internal energy decreases

Explanation

To solve the question "If a gas, at constant temperature and pressure expands, then its...", we can analyze the situation using the principles of thermodynamics, particularly the first law of thermodynamics.

### Step-by-Step Solution:

1. **Understanding the First Law of Thermodynamics**:
The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W):
\[ \Delta U = Q - W \]

2. **Identifying the Conditions**:
The problem states that the gas is expanding at constant temperature and constant pressure. This means we are dealing with an isothermal (constant temperature) and isobaric (constant pressure) process.

3. **Analyzing Internal Energy for an Ideal Gas**:
For an ideal gas, the internal energy (U) is primarily a function of temperature. Therefore, if the temperature remains constant during the expansion, the internal energy does not change:
\[ \Delta U = 0 \quad \text{(since temperature is constant)} \]

4. **Heat and Work Relationship**:
Since the internal energy remains constant (ΔU = 0), we can rearrange the first law of thermodynamics equation:
\[ 0 = Q - W \implies Q = W \]
This indicates that the heat absorbed by the system (Q) is equal to the work done by the system (W) during the expansion.

5. **Conclusion**:
Therefore, when a gas expands at constant temperature and pressure, its internal energy remains the same.

### Final Answer:
If a gas, at constant temperature and pressure expands, then its internal energy remains the same.

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