Question

A body cools from 50.0°C to 49.9°C in 5s. How long will it take to cool from 40.0°C to 39.9°C? Assume the temperature of surroundings to be 30.0°C and Newton’s law of cooling to be valid:

• A. 2.5 s
• B. 10 s
• C. 20 s
• D. 5 s

Hint:

The time to cool by a certain temperature is inversely proportional to the temperature difference when using Newton’s Law of Cooling.

Answer 1

The Correct Option is A

Step 1: According to Newton’s law of cooling, the rate of cooling is proportional to the temperature difference.
Step 2: Since the temperature difference for the second case is smaller, the cooling time will be proportionally longer. Using the rate of cooling from the first case, we can calculate the time required for the second cooling process.

Final Answer: \[ \boxed{2.5 \, \text{s}} \]