Answer to Question #94780 in Molecular Physics | Thermodynamics for Taiwo Michael

Question

If it takes 10minutes for the temperature of initial to fall from 100°c to 80°c within a surround temperature of 30°c. Calculate the Temperature of the initial after 30minutes

Answer 1

We have:

$$T-T_a=A\exp{(-kt)}$$

The initial conditions:

$$100-30=A\to A=70\degree C$$

Now,

$$80-30=70\exp{(-k(10))}$$

$$k=0.1\ln{1.4}$$

So, temperature of the initial after 30 minutes:

$$T=30+70\exp{(-0.1\ln{1.4}(30))}=55.5\degree C$$