The rate of cooling of a body depends on –

Options

A. The difference of temperature of the body and the surrounding.
B. Area of surface of body.
C. Nature of surface of body.
D. All of the above.

Answer

To determine the factors on which the rate of cooling of a body depends, we can refer to Stefan's Law of thermal radiation. Here’s a step-by-step solution:

### Step 1: Understand Stefan's Law
Stefan's Law states that the power radiated by a body is proportional to the fourth power of its absolute temperature minus the fourth power of the absolute temperature of its surroundings. Mathematically, this is expressed as:

\[ P = \sigma A e (T_b^4 - T_s^4) \]

Where:
- \( P \) = Power (rate of heat loss)
- \( \sigma \) = Stefan-Boltzmann constant (\(5.67 \times 10^{-8} \, \text{W/m}^2 \text{K}^4\))
- \( A \) = Surface area of the body
- \( e \) = Emissivity of the body
- \( T_b \) = Absolute temperature of the body
- \( T_s \) = Absolute temperature of the surroundings

### Step 2: Identify the Factors Affecting Cooling Rate
From the equation above, we can identify the factors that affect the rate of cooling:

1. **Temperature Difference**: The difference between the temperature of the body and the surrounding environment (\( T_b - T_s \)) greatly influences the rate of cooling. A larger temperature difference results in a higher rate of heat loss.

2. **Surface Area**: The larger the surface area of the body, the more heat can be radiated away. Thus, the area \( A \) is a crucial factor.

3. **Emissivity**: The nature of the surface of the body, represented by emissivity \( e \), also affects the cooling rate. Different materials and surface textures (e.g., rough vs. smooth, black vs. shiny) have different emissivities, impacting how effectively they radiate heat.

### Step 3: Conclusion
Based on the analysis, we conclude that the rate of cooling of a body depends on:
- The temperature difference between the body and its surroundings
- The surface area of the body
- The emissivity of the body

Thus, the correct answer is that the rate of cooling depends on all of the above factors.

### Final Answer:
The rate of cooling of a body depends on:
1. The temperature difference between the body and its surroundings.
2. The surface area of the body.
3. The nature of the surface (emissivity).