Question

A body takes $T \, $ minutes to cool from $62 \,{}^\circ C$ to $61 \,{}^\circ C$ when the surrounding temperature is $30 \,{}^\circ C$ . The time taken by the body to cool from $46 \,{}^\circ C \, $ to $45.5 \,{}^\circ C$ is

• A. Greater than T minutes
• B. Equal to T minutes
• C. Less than T minutes
• D. None of these

Answer 1

Answer: (B)

According to Newton's law of cooling
$\frac{\theta _{1} - \theta _{2}}{t} \, \propto \left[\frac{\theta _{1} + \theta _{2}}{2} - \theta \right]$
For the first condition
$\frac{62 - 61}{T} \, \propto \left[\frac{62 + 61}{2} - 30\right]$ (i)
And for the second condition
$\frac{46 - 45.5}{t} \propto \left[\frac{46 + 45.5}{2} - 30\right]$ (ii)
By solving equation (i) and (ii), we get t = T minutes.