Newton's law of cooling is a special case of

Options

A. Wien's displacement law
B. Krichhoff's law
C. Stefan's law
D. planck's law.

Explanation

To solve the question "Newton's law of cooling is a special case of which law?" we will analyze the options provided and understand the relationship between Newton's law of cooling and the Stefan-Boltzmann law.

### Step-by-Step Solution:

1. **Understanding Newton's Law of Cooling**:
- Newton's law of cooling states that the rate of cooling of a body is directly proportional to the temperature difference between the body and its surroundings. Mathematically, it can be expressed as:
\[ \frac{dQ}{dt} \propto (T_{\text{body}} - T_{\text{surrounding}}) \]
- Here, \(T_{\text{body}}\) is the temperature of the body and \(T_{\text{surrounding}}\) is the temperature of the surroundings.

2. **Understanding Stefan-Boltzmann Law**:
- The Stefan-Boltzmann law states that the total energy radiated per unit surface area of a black body per unit time is proportional to the fourth power of the black body's absolute temperature. It can be expressed as:
\[ \frac{dQ}{dt} = \epsilon \sigma A (T^4 - T_{\text{surrounding}}^4) \]
- Here, \(\epsilon\) is the emissivity of the body, \(\sigma\) is the Stefan-Boltzmann constant, \(A\) is the surface area, and \(T\) and \(T_{\text{surrounding}}\) are the absolute temperatures of the body and surroundings, respectively.

3. **Condition for Small Temperature Differences**:
- When the temperature difference between the body and the surroundings is small, we can approximate the fourth power term using a Taylor expansion. If we assume \(T_{\text{surrounding}} = 0\) for simplicity, we can express the temperature of the body as:
\[ T_{\text{body}} = T_{\text{surrounding}} + \Delta T \]
- In this case, the Stefan-Boltzmann law can be simplified to show that the rate of cooling becomes proportional to the temperature difference, which aligns with Newton's law of cooling.

4. **Conclusion**:
- Therefore, we conclude that Newton's law of cooling is indeed a special case of the Stefan-Boltzmann law when the temperature difference is small.

5. **Final Answer**:
- Newton's law of cooling is a special case of the **Stefan-Boltzmann law**.