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

Options

A. Enthropy increases and then decrease
B. Internal energy increases
C. Internal energy remains the same
D. Internal energy decreases

Answer

To solve the question about the behavior of a gas during expansion at constant temperature and pressure, we can follow these steps:

### 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). Mathematically, this is expressed as:
\[ \Delta U = q - w \]

2. **Identifying Conditions**:
In this scenario, the gas is expanding at constant temperature and pressure. This means that during the expansion, the temperature (T) and pressure (P) do not change.

3. **Work Done During Expansion**:
The work done by the gas during expansion can be expressed as:
\[ w = -P \Delta V \]
where ΔV is the change in volume. Since the gas is expanding, ΔV is positive, making w negative (indicating work is done by the system).

4. **Heat Transfer at Constant Temperature**:
At constant temperature, for an ideal gas, the internal energy (U) is primarily a function of temperature. Therefore, if the temperature is constant, the change in internal energy (ΔU) is zero:
\[ \Delta U = 0 \]

5. **Substituting into the First Law**:
Since ΔU = 0, we can substitute this into the first law equation:
\[ 0 = q - w \]
Rearranging gives:
\[ q = w \]
This means that the heat added to the system is equal to the work done by the system.

6. **Conclusion**:
Since the internal energy remains unchanged during the expansion at constant temperature and pressure, the correct statement is that the internal energy of the gas remains the same.

### Final Answer:
The internal energy of the gas remains the same during the expansion at constant temperature and pressure.

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