Question

If the body cools from \( 135^\circ C \) to \( 80^\circ C \) at room temperature of \( 25^\circ C \) in 60 minutes, then the temperature of the body after 2 hours is

• A. \( 52.5^\circ C \)
• B. \( 10.5^\circ C \)
• C. \( 52.75^\circ C \)
• D. \( 10.75^\circ C \)

Hint:

Use Newton’s Law of Cooling to model temperature changes over time. The constant \( k \) can be determined from the initial conditions.

Answer 1

The Correct Option is A

Step 1: Apply Newton's Law of Cooling.
Newton’s Law of Cooling states that the rate of change of temperature of an object is proportional to the difference between the temperature of the object and the ambient temperature: \[ \frac{dT}{dt} = -k(T - T_{\text{room}}) \] where \( T_{\text{room}} = 25^\circ C \). The object cools from \( 135^\circ C \) to \( 80^\circ C \) in 60 minutes. Using this information, we can find the constant of proportionality \( k \).
Step 2: Solve for \( k \).
After solving for \( k \), we use the equation to determine the temperature after 2 hours.
Step 3: Conclusion.
The temperature after 2 hours is found to be \( 52.5^\circ C \), corresponding to option (A).