The specific heat of gas

Options

A. has only two values `Cp` & `Cv`
B. has a unique value of given temperature
C. can have any values from `O` to `prop`
D. depends upon the mass of the gas

Answer

To solve the question regarding the specific heat of gas, we need to understand the concepts of specific heat at constant pressure (Cp) and constant volume (Cv), as well as how specific heat can vary under different conditions.

### Step-by-Step Solution:

1. **Understanding Specific Heat**:
- Specific heat is defined as the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin).
- For gases, specific heat can be categorized into two types:
- **Cp**: Specific heat at constant pressure.
- **Cv**: Specific heat at constant volume.

2. **Values of Specific Heat**:
- The specific heat values (Cp and Cv) are unique for a given gas at a specific temperature. However, they can vary depending on the process the gas undergoes.
- For example, during an **adiabatic process**, no heat is exchanged with the surroundings, which affects how we consider specific heat.

3. **Behavior in Different Processes**:
- In an **isothermal process** (constant temperature), the specific heat can be considered infinite because the gas does not change temperature despite heat being added or removed.
- In contrast, during an **adiabatic process**, the specific heat is not defined in the same way because there is no heat transfer.

4. **Range of Specific Heat Values**:
- The specific heat of a gas can theoretically take any value from 0 to infinity depending on the conditions and processes involved.
- This means that while Cp and Cv are specific values for a gas at a given temperature, the specific heat can vary widely under different conditions.

5. **Conclusion**:
- Therefore, the specific heat of a gas is not limited to just two values (Cp and Cv) and can indeed attain any value from 0 to infinity depending on the mass of the gas and the specific process it undergoes.

### Final Answer:
The specific heat of a gas can attain any value from 0 to infinity depending on the mass of the gas and the process it undergoes, making option C the correct choice.