According to Newton’s law of cooling, the rate of cooling of a body is proportional to `(Deltatheta)^(n)` , where `Deltatheta`is the difference of the temperature of the body and the surrounding, and n is equal to :

Options

A. One
B. two
C. three
D. four

Explanation

To solve the question regarding Newton's law of cooling and the value of \( n \), we can follow these steps:

### Step-by-Step Solution

1. **Understand 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. This can be mathematically represented as:
\[ \text{Rate of cooling} \propto \Delta \theta \]
where \( \Delta \theta \) is the temperature difference.

2. **Express the Proportionality in Equation Form**:
We can express the above statement in equation form by introducing a constant of proportionality \( k \):
\[ \text{Rate of cooling} = -k \Delta \theta \]
The negative sign indicates that the temperature of the body is decreasing.

3. **Compare with Given Form**:
According to the question, the rate of cooling is also given as proportional to \( (\Delta \theta)^n \):
\[ \text{Rate of cooling} \propto (\Delta \theta)^n \]
From the two expressions, we can equate them:
\[ -k \Delta \theta = C (\Delta \theta)^n \]
where \( C \) is another constant.

4. **Determine the Value of \( n \)**:
For the two expressions to be equivalent, the powers of \( \Delta \theta \) must match. Thus, we can conclude:
\[ n = 1 \]

5. **Final Answer**:
Therefore, the value of \( n \) in the context of Newton's law of cooling is:
\[ n = 1 \]