Question

The temperature loss from a hot object in contact with a colder object is directly proportional to the 4th power of temperature difference between the objects. The directly proportional the time of contact as well. How much heat loss happens when unit 1 at T, and unit 2 at T₂ are put in contact (assume T₁>T2) for n units of time?

Answer 1

Rate of heat loss

Explanation:

• Rate of heat loss (dQ) according to the mentioned data should be :

      $\frac{dQ}{dn} = A e \sigma (T_1^4 - T_2^4)$  , where A is the surface area , e is called the emissivity and sigma $\sigma$ is the Stefan's Boltzmann constant.  Also dn is the time in seconds as given .

• However, this equation is for radiative heat loss in which heat loss occurs due to radiation where 2 bodies are not in contact with each other.
• But in the question above , it says, time of contact of hot and cold body is n units , which means bodies are in physical contact . Therefore , in this case heat loss is given by

                          $\frac{Q}{n} = \frac{kA(T_2-T_1)}{d}$  

where k is the thermal conductivity and d is the thickness of the material.