The rate of cooling of a heated quantity of liquid in an enclosure depends on the

Analysis of the Question

This question tests your understanding of Newton’s Law of Cooling. The law states that the rate at which an object (or liquid) loses heat to its surroundings is proportional to the difference in temperature between the object and its surroundings.

Concept Explanation

Newton’s Law of Cooling is expressed by the formula:

Where:

• $\frac{dQ}{dt}$ is the rate of cooling (heat loss per unit time).
• $k$ is a constant depending on the nature of the surface and the enclosure.
• $T$ is the temperature of the liquid.
• $T_s$ is the temperature of the surroundings (the enclosure).

From this formula, you can see that the rate of cooling depends directly on the temperature difference between the liquid and the enclosure. If the temperature of the enclosure ($T_s$) changes, the rate of cooling will change accordingly.

Step-by-Step Solution

1. Identify the variables: The rate of cooling is determined by the temperature gradient between the hot body and the environment.
2. Evaluate the options: • A (Pressure of the liquid): Pressure does not directly dictate the rate of heat transfer in this context. • B (Temperature in the enclosure): As shown in the formula, the temperature of the surroundings ($T_s$) is a primary factor in determining how fast the liquid cools. • C (Pressure of the enclosure): While pressure can affect boiling points, it is not the primary factor for the rate of cooling in a standard enclosure. • D (Volume of the liquid): While volume affects the total heat capacity, the rate of cooling is primarily governed by the temperature difference and surface area, not the volume itself.

Conclusion

The rate of cooling is fundamentally dependent on the temperature difference between the liquid and its surroundings (the enclosure). Therefore, the temperature of the enclosure is the correct factor among the choices provided.

Exam Tip

When you see questions about "rate of cooling," always look for keywords related to temperature difference. Remember that the larger the difference between the hot object and the room (enclosure), the faster the object will cool down!