Question

A bowl filled with very hot water cools from \(98^{\circ}\text{C}\) to \(86^{\circ}\text{C}\) in 2 minutes when the room temperature is \(22^{\circ}\text{C}\). How long it will take to cool from \(75^{\circ}\text{C}\) to \(69^{\circ}\text{C}\) ?

• A. \(0.5\) minute
• B. \(1.4\) minute
• C. \(1\) minute
• D. \(2\) minute

Hint:

The rate of fall equals k times the excess over room temperature, using the mean temperature.

Answer 1

The Correct Option is B

Step 1: Eliminate k
Divide the two equations: $\frac{12/2}{6/t} = \frac{70}{50}$.

Step 2: Solve
The left side simplifies: $\frac{12/2}{6/t} = \frac{6}{6/t} = t$. So $t = \frac{70}{50} = 1.4$ min. Option (B).

Final Answer:
1.4 minutes. \[ \boxed{\text{(B)}\ 1.4\ \text{minute}} \]