According to ‘Newton’s Law of cooling’, the rate of cooling of a body is proportional to the

Options

A. Temperature of the body
B. Temperature of the surrounding
C. Fourth power of the temperature of the body
D. Difference of the temperature of the body and the surroudings

Answer

To solve the question regarding Newton's Law of Cooling, we can follow these steps:

### Step 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 between its own temperature and the temperature of its surroundings.

### Step 2: Define the Variables
Let:
- \( T_2 \) = Initial temperature of the body
- \( T_1 \) = Final temperature of the body after time \( T \)
- \( T_{\theta} \) = Temperature of the surroundings

### Step 3: Establish the Rate of Cooling
According to the law, the rate of cooling can be expressed mathematically as:
\[ \frac{dT}{dt} \propto (T - T_{\theta}) \]
where \( T \) is the temperature of the body at any time \( t \).

### Step 4: Express the Mean Temperature Difference
The mean temperature difference can be expressed as:
\[ \text{Mean Temperature Difference} = \frac{(T_2 + T_1)}{2} - T_{\theta} \]

### Step 5: Identify the Proportionality
From the above, we can conclude that the rate of cooling is proportional to the temperature difference between the body and the surroundings:
\[ \text{Rate of Cooling} \propto (T - T_{\theta}) \]

### Step 6: Conclusion
Thus, according to Newton's Law of Cooling, the rate of cooling of a body is proportional to the difference between the temperature of the body and the temperature of the surroundings.

### Final Answer
The correct statement is that the rate of cooling of a body is proportional to the difference between the temperature of the body and the surrounding temperature.

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