Which of the following is not expressed correctly with respect to units?

Options

A. Specific heat `to J Kg^(-1) K^(-1)`
B. Entropy `to JK^(-1)`
C. Thermal capacity `to J Kg^(-1)`
D. Temperature gradient `to m^(-1) K`

Answer

To determine which of the given options is not expressed correctly with respect to units, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Option 1: Specific Heat**
- Specific heat is defined as the amount of heat required to raise the temperature of 1 kilogram of a substance by 1 Kelvin.
- The SI unit of specific heat is indeed joule per kilogram per Kelvin (J/kg·K).
- **Conclusion:** This option is correctly expressed.

2. **Option 2: Entropy**
- Entropy is a measure of the randomness or disorder of a system.
- The SI unit of entropy is joule per Kelvin (J/K).
- **Conclusion:** This option is also correctly expressed.

3. **Option 3: Thermal Capacity**
- Thermal capacity (also known as heat capacity) is defined as the amount of heat required to change the temperature of an object by 1 Kelvin.
- The SI unit of thermal capacity is joule per Kelvin (J/K), not joule per kilogram (J/kg).
- **Conclusion:** This option is not correctly expressed.

4. **Option 4: Temperature Gradient**
- The temperature gradient is defined as the rate of change of temperature with respect to distance.
- The SI unit of temperature gradient is Kelvin per meter (K/m).
- **Conclusion:** This option is correctly expressed.

### Final Answer:
The option that is not expressed correctly with respect to units is **Option 3: Thermal Capacity** (it should be expressed in joules per Kelvin, not joules per kilogram).

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