The specific heat of a gas in an isothermal process is

Options

A. infinite
B. zero
C. negative
D. remains constant

Answer

To solve the question regarding the specific heat of a gas in an isothermal process, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Isothermal Process**:
- An isothermal process is one in which the temperature of the system remains constant. This means that during the process, there is no change in temperature (ΔT = 0).

2. **Definition of Specific Heat Capacity**:
- Specific heat capacity (S) is defined as the amount of heat (Q) required to raise the temperature of 1 kg of a substance by 1 Kelvin (or 1 degree Celsius). Mathematically, it can be expressed as:
\[ S = \frac{Q}{m \cdot \Delta T} \]
where:
- \( S \) = specific heat capacity
- \( Q \) = heat added or removed
- \( m \) = mass of the substance
- \( \Delta T \) = change in temperature

3. **Applying the Isothermal Condition**:
- Since the process is isothermal, we have ΔT = 0. Substituting this into the specific heat capacity formula gives:
\[ S = \frac{Q}{m \cdot 0} \]

4. **Analyzing the Equation**:
- In the equation, the denominator becomes zero (because ΔT = 0). Division by zero is undefined in mathematics, but in the context of specific heat, this implies that an infinite amount of heat would be required to change the temperature of the gas, which cannot happen in an isothermal process.

5. **Conclusion**:
- Therefore, we conclude that the specific heat capacity of a gas in an isothermal process is infinite.

### Final Answer:
- The specific heat of a gas in an isothermal process is **infinite** (Option A).