Specific heat of a gas during an isothermal change is

Options

A. Zero
B. Positive
C. negative
D. infinity

Explanation

To determine the specific heat of a gas during an isothermal change, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Isothermal Process**:
- An isothermal process is defined as a thermodynamic process in which the temperature (T) remains constant. Therefore, the change in temperature (ΔT) is equal to 0.

2. **Recall the Formula for Specific Heat**:
- The specific heat (C) can be defined using the formula:
\[ \Delta Q = m \cdot C \cdot \Delta T \]
where:
- ΔQ is the heat added or removed,
- m is the mass of the substance,
- C is the specific heat capacity,
- ΔT is the change in temperature.

3. **Substitute ΔT in the Formula**:
- Since we are dealing with an isothermal process, we know that ΔT = 0. Substituting this into the specific heat formula gives:
\[ \Delta Q = m \cdot C \cdot 0 \]
- This simplifies to:
\[ \Delta Q = 0 \]

4. **Rearranging the Formula**:
- To find the specific heat (C), we can rearrange the formula:
\[ C = \frac{\Delta Q}{m \cdot \Delta T} \]
- Substituting ΔT = 0 into this equation results in:
\[ C = \frac{\Delta Q}{m \cdot 0} \]

5. **Evaluate the Expression**:
- Since we cannot divide by zero, this expression implies that C approaches infinity. Therefore, we conclude:
\[ C = \infty \]

6. **Conclusion**:
- The specific heat of a gas during an isothermal change is infinite.

### Final Answer:
- The specific heat of a gas during an isothermal change is **infinity**.