Question

A body initially at 80 degree Celsius cools to 64 degree Celsius in 5 minutes and to 52 degree Celsius in 10 minutes. The temperature of the body after 15 minutes will be.......

Answer 1

According to Newton law of cooling

$\frac{dT}{dt}=K[T_t-T_0];T_f=\frac{(T_F+T_i)}{2}$

$\frac{16}{5}=K[72-Ts]$

$\frac{12}{5}=K[58-Ts]$

$dividing\left(1\right)with\left(2\right)$

$T_S={16}^{\theta }c$

$now,\frac{16}{5}=K\left[56\right]$

$K=\frac{2}{35}$

$\frac{(52-T)}{5}=\frac{2}{35}(\frac{T}{2}+26-16)$

$52\times 7-7T=T+20$

$T=\frac{344}{8}={43}^{\theta }C$