Question

The initial temperature of a body is 80 ^oC. Its temperature falls to 64 ^oC in 5 minutes and to 52 ^oC in next 10 minutes. If the temperature of surrounding is 7n ^oC, value of n is

Answer 1

According to Newton’s law:$\frac{{\theta }_1-{\theta }_2}{t}=k[\frac{{\theta }_1+{\theta }_2}{2}-{\theta }_0]$
Initially, $\frac{(80-64)}{5}=K[\frac{80+64}{2}-{\theta }_0]$
$\Rightarrow$ $3.2=K[72-{\theta }_0]$
Finally, $\frac{(64-52)}{10}=K[\frac{64+52}{2}-{\theta }_0]$
$\Rightarrow$ $1.2=K[58-{\theta }_0]$
On solving above two equations, we get ${\theta }_0=49{}^{o}C$.
Hence, n = 7.