Question

Rate of cooling of a body is \(0.2^\circ \text{C/min}\) when excess temperature is \(20^\circ \text{C}\). The proportionality constant \( k \) is:

• A. \( 0.005 \, \text{min}^{-1} \)
• B. \( 0.01 \, \text{min}^{-1} \)
• C. \( 0.05 \, \text{min}^{-1} \)
• D. \( 0.2 \, \text{min}^{-1} \)

Hint:

Newton’s Law of Cooling is valid for small temperature differences between the body and its surroundings.

Answer 1

The Correct Option is B

Newton's Law of Cooling states: \[ \text{Rate of cooling} = k (\Delta T), \] where \( k \) is the proportionality constant and \( \Delta T \) is the excess temperature. Given: \[ \text{Rate of cooling} = 0.2 \, \text{°C/min}, \quad \Delta T = 20^\circ \text{C}. \] Solving for \( k \): \[ k = \frac{\text{Rate of cooling}}{\Delta T} = \frac{0.2}{20} = 0.01 \, \text{min}^{-1}. \] ---