If a gas is heated at constant pressure, its isothermal compressibility

Options

A. remains constant
B. increases linearly
C. decreases linearly with temperature
D. decreases inversely with temperature

Answer

To solve the question regarding the isothermal compressibility of a gas heated at constant pressure, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Isothermal Compressibility**:
The isothermal compressibility (κ) is defined as:
\[ \kappa = -\frac{1}{V} \left( \frac{dV}{dP} \right)_{T} \]
where \(V\) is the volume, \(P\) is the pressure, and \(T\) is the temperature.

2. **Identify the Conditions**:
The problem states that the gas is heated at constant pressure. This means that the pressure \(P\) does not change during the heating process.

3. **Use the Ideal Gas Law**:
According to the ideal gas law:
\[ PV = nRT \]
Rearranging this gives:
\[ V = \frac{nRT}{P} \]
Since \(P\) is constant, we can analyze how \(V\) changes with \(T\).

4. **Differentiate Volume with Respect to Pressure**:
Since \(P\) is constant, when we differentiate \(V\) with respect to \(P\):
\[ \frac{dV}{dP} = 0 \]
This is because \(V\) does not change with \(P\) when \(T\) is increased at constant pressure.

5. **Substitute into the Compressibility Formula**:
Now, substituting \( \frac{dV}{dP} = 0 \) into the isothermal compressibility formula:
\[ \kappa = -\frac{1}{V} \cdot 0 = 0 \]

6. **Conclusion**:
Therefore, the isothermal compressibility of the gas when heated at constant pressure is:
\[ \kappa = 0 \]

### Final Answer:
The isothermal compressibility of a gas heated at constant pressure is 0.

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