Question

A body initially at 80${}^{\circ }$C cools to 64${}^{\circ }$C in 5 min and to 52${}^{\circ }$C in 10 min. The temperature of the surrounding is

• A. 26${}^{\circ }$C
• B. 16${}^{\circ }$C
• C. 36${}^{\circ }$C
• D. 40${}^{\circ }$C

Answer 1

Answer: (B)

According to Newton’s law of cooling
$\frac{{\theta }_1-{\theta }_2}{t}=K\left[\frac{{\theta }_1+{\theta }_2}{2}-{\theta }_0\right]$
In the first case, $\frac{80-64}{5}=K\left[\frac{80+64}{2}-{\theta }_0\right]$
or$3.2=K\left[58-{\theta }_0\right]....\left(i\right)$
In the second case,$\frac{64-52}{5}=K\left[\frac{64+52}{2}-{\theta }_0\right]$
or$2.4=K\left[58-{\theta }_0\right]....\left(ii\right)$
Dividing (i) by (ii), we get $\frac{3.2}{2.4}=\frac{72-{\theta }_0}{58-{\theta }_0}$
or $185.6-3.2{\theta }_0=172.8-2.4{\theta }_0$or ${\theta }_0=16^{\circ }C$