Question

The temperature of a body decreased from ${200}^o$ to ${100}^o$ in $1$ hour. Determine how many degrees the body cooled in one hour more if the environment temperature is $0^o$ ?

• A. ${30}^o$
• B. ${40}^o$
• C. ${50}^o$
• D. ${60}^o$

Answer 1

The correct option is C ${50}^o$

We know from NEWTONS LAW OF COOLING THAT,

$-\frac{dT}{dt}=k(T-T_s)$,

Where $T_s$ is the environment temperature,

Here environment temperature is $0$,

Now solving the differential equation gives,

$\ln \left(\frac{T_2-T_s}{T_1-T_s}\right)=-kt$,$k$ is a constant,

Substituting the given values in the equation gives,

$\ln 2=-k$,

After one more hour,,

$\ln \left(\frac{200}{T}\right)=2\ln 2$,

$⟹T={50}^0$