Question

The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is 290K and the metal temperature drops from 370K to 330K in 10 minutes, then the time required to drop the temperature up to 295K is

• A. 40 min
• B. 20 min
• C. 35 min
• D. 30 min

Hint:

For problems involving cooling, apply Newton's Law of Cooling, and use the given temperatures to solve for the required time.

Answer 1

The Correct Option is A

Step 1: Understand the cooling law.
The problem follows Newton's Law of Cooling, which states that the rate of cooling is proportional to the temperature difference between the object and the surrounding medium. The equation governing this is: \[ \frac{dT}{dt} = -k(T - T_{\text{air}}) \] where \( T_{\text{air}} \) is the surrounding air temperature, and \( k \) is the proportionality constant.

Step 2: Solve using the given data.
Using the given temperatures, we set up the equation for the cooling process and solve for \( k \). Using this value, we can calculate the time required to cool from 330K to 295K. The time comes out to be 40 minutes.

Step 3: Conclusion.
Thus, the required time is 40 minutes, corresponding to option (A).