Question

In a room where temperature is $30^{\circ} C$, a body cools from $61^{\circ} C$ to $59^{\circ} C$ in 4 minutes. The time taken by the body to cool from $51^{\circ} C$ to $49^{\circ} C$ will be:

• A. 4 minute
• B. 6 minute
• C. 5 minute
• D. 8 minute

Answer 1

Answer: (B)

Rate of cooling $\alpha$ differenc in temperature
$\frac{\Delta T}{\Delta t} \propto \Delta \theta$
$\Rightarrow \frac{\Delta T}{\Delta t}=K \Delta \theta$
$\Rightarrow \Delta T=K \Delta \theta \cdot \Delta T$
In first case:
$\Delta T =61-59=2$
$\Rightarrow \Delta \theta =60^{\circ}-30^{\circ}=30^{\circ}$
$\Delta t =4\, \min$
$\Rightarrow K =\frac{\Delta T}{\Delta \theta \Delta t}=\frac{2}{30 \times 4}=\frac{1}{60}$
For second case :
$d T =2$
$\Delta \theta =50-30=20$
$\Rightarrow dt =\frac{d T}{K \Delta \theta}=\frac{2}{\frac{1}{60} \times 20}=6\, \min$