If the thermal capacity of a body is infinity, then

Options

A. heat can never be added to it
B. heat can never be extracted from it
C. the temperature of the body cannot be altered by adding or extracting any amount of heat
D. it has infinite amount of heat

Answer

To solve the question, "If the thermal capacity of a body is infinity, then," we will analyze the implications of an infinite thermal capacity step by step.

### Step-by-Step Solution:

1. **Understanding Thermal Capacity**:
- Thermal capacity (or heat capacity) is defined as the amount of heat required to change the temperature of a body by one degree Celsius (or one Kelvin). Mathematically, it is expressed as:
\[ C = \frac{Q}{\Delta T} \]
where \(C\) is the thermal capacity, \(Q\) is the heat added or removed, and \(\Delta T\) is the change in temperature.

2. **Infinite Thermal Capacity**:
- If the thermal capacity of a body is infinite, it implies that no matter how much heat \(Q\) is added or removed, the change in temperature \(\Delta T\) remains zero. This can be expressed as:
\[ C = \frac{Q}{0} \rightarrow \text{undefined or infinite} \]

3. **Implications of Infinite Thermal Capacity**:
- Since \(\Delta T\) is zero, it means that the temperature of the body does not change regardless of the amount of heat added or extracted. Therefore, the body can absorb or release heat without any change in temperature.

4. **Evaluating the Options**:
- **Option 1**: Heat can never be added to it. (Incorrect)
- **Option 2**: Heat can never be extracted from it. (Incorrect)
- **Option 3**: The temperature of the body cannot be altered by adding or extracting any amount of heat. (Correct)
- **Option 4**: It has an infinite amount of heat. (Incorrect)

5. **Conclusion**:
- The correct answer is that if the thermal capacity of a body is infinite, then the temperature of the body cannot be altered by adding or extracting any amount of heat. Thus, option 3 is the correct choice.