What does it mean , If specific heat of a substance is infinite

Options

A. heat is given out
B. heat is taken in
C. no change in temperature whether heat is taken in or given out
D. all of the above

Answer

To understand what it means if the specific heat of a substance is infinite, we can break it down step by step:

### Step 1: Definition of Specific Heat
Specific heat (s) is defined as the amount of heat (Q) required to change the temperature of a unit mass (m) of a substance by one degree Celsius (or one Kelvin). Mathematically, this can be expressed as:
\[ Q = m \cdot s \cdot \Delta T \]
where:
- \( Q \) = heat added or removed
- \( m \) = mass of the substance
- \( s \) = specific heat
- \( \Delta T \) = change in temperature

### Step 2: Understanding Infinite Specific Heat
If the specific heat of a substance is infinite, it implies that an infinite amount of heat is required to change the temperature of that substance by just one degree Celsius. This can be interpreted as follows:
- For any finite amount of heat added or removed, the temperature change (\( \Delta T \)) would be zero.

### Step 3: Condition for Infinite Specific Heat
To achieve an infinite specific heat, the equation \( Q = m \cdot s \cdot \Delta T \) suggests that for \( s \) to approach infinity, the change in temperature (\( \Delta T \)) must approach zero. This scenario is characteristic of an isothermal process, where the temperature remains constant despite heat being added or removed.

### Step 4: Conclusion
Therefore, if the specific heat of a substance is infinite, it means that the substance can absorb or release heat without any change in temperature. This is typically seen in theoretical scenarios or ideal substances, as real materials always have finite specific heats.

### Summary
In conclusion, an infinite specific heat indicates that the substance can undergo heat transfer without any temperature change, which is a characteristic of an isothermal process.

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