Which of the law can be understood in terms of Stefan's law

Options

A. Wien's displacement law
B. Kirhoff's law
C. Newton's law of cooling
D. Planck's law

Explanation

To solve the question "Which of the law can be understood in terms of Stefan's law?", we will analyze the relationship between Stefan's law and Newton's law of cooling step by step.

### Step-by-Step Solution:

1. **Understanding Stefan's Law**:
- Stefan's law states that the rate of heat transfer (dQ/dt) is proportional to the difference in the fourth power of the absolute temperatures of two bodies. The mathematical expression is given by:
\[ \frac{dQ}{dt} = \sigma \epsilon A (T_1^4 - T_2^4) \]
- Here, \( \sigma \) is the Stefan-Boltzmann constant, \( \epsilon \) is the emissivity of the surface, \( A \) is the area, \( T_1 \) and \( T_2 \) are the absolute temperatures of the two bodies.

2. **Rearranging the Equation**:
- We can express \( T_1 \) in terms of \( T_2 \) and a small temperature difference \( \Delta T \):
\[ T_1 = T_2 + \Delta T \]
- Substituting this into the Stefan's law equation gives:
\[ \frac{dQ}{dt} = \sigma \epsilon A \left((T_2 + \Delta T)^4 - T_2^4\right) \]

3. **Expanding Using Binomial Theorem**:
- For small \( \Delta T \), we can use the binomial expansion:
\[ (T_2 + \Delta T)^4 \approx T_2^4 + 4T_2^3 \Delta T \]
- Thus, we can simplify the equation:
\[ \frac{dQ}{dt} \approx \sigma \epsilon A \left(4T_2^3 \Delta T\right) \]

4. **Identifying the Proportionality**:
- From the simplified equation, we can see that:
\[ \frac{dQ}{dt} \propto \Delta T \]
- This indicates that the rate of heat transfer is directly proportional to the change in temperature \( \Delta T \).

5. **Connecting to Newton's Law of Cooling**:
- Newton's law of cooling states that the rate of heat loss of a body is directly proportional to the difference in temperature between the body and its surroundings. This can be expressed as:
\[ \frac{dQ}{dt} \propto (T - T_{surroundings}) \]
- Therefore, we can conclude that Stefan's law can be used to derive Newton's law of cooling, as both laws describe the relationship between heat transfer and temperature difference.

### Final Answer:
The law that can be understood in terms of Stefan's law is **Newton's law of cooling**.

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