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 \( n \) in the equation where the rate of cooling is proportional to \( (\Delta \theta)^n \), 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 change of temperature of a body is proportional to the difference in temperature between the body and its surroundings.

2. **Set Up the Equation**:
Mathematically, this can be expressed as:
\[ -\frac{dT}{dt} \propto (T_b - T_s) \]
where \( T_b \) is the temperature of the body and \( T_s \) is the temperature of the surroundings.

3. **Express the Proportionality**:
We can replace the proportionality with an equality by introducing a constant \( k \):
\[ -\frac{dT}{dt} = k (T_b - T_s) \]

4. **Define \( \Delta \theta \)**:
Here, \( \Delta \theta \) is defined as the temperature difference:
\[ \Delta \theta = T_b - T_s \]

5. **Identify the Power**:
In the equation \( -\frac{dT}{dt} = k \Delta \theta \), we see that the temperature difference \( \Delta \theta \) is raised to the power of 1. Therefore, we can conclude that:
\[ n = 1 \]

6. **Final Answer**:
Thus, according to Newton's law of cooling, the value of \( n \) is:
\[ n = 1 \]