Question

If the time taken by a hot body to cool from $50^{\circ}$C to $40^{\circ}$C is 10 minutes when the surrounding temperature is $25^{\circ}$C. then the time taken for it to cool from $40^{\circ}$C to $30^{\circ}$C when the surrounding temperature is $15^{\circ}$C, is

• A. 40 min
• B. 10 min
• C. 5 min
• D. 15 min

Answer 1

Answer: (B)

10 min

Answer 2

We know that,
$\frac{d Q}{d t} \propto\left[\frac{\theta_{1}+\theta_{2}}{2}-\theta_{0}\right]$
$\frac{10}{10} \propto\left[\frac{50-40}{2}-25\right]$
$\frac{10}{10} \propto[45-25]\,\,\,\,\,\dots(i)$
Similarly,
$\frac{10}{t} \propto\left[\frac{40+30}{2}-15\right]$
$\frac{10}{t} \propto[35-15]\,\,\,\,\,\dots(ii)$
Now, divide E (i) by E (ii), we get
$\frac{t}{10} =\frac{20}{20}$
$t =10 \,min$