An object with surface area A is placed in an oven which is maintaining temperat

Question

An object with surface area A is placed in an oven which is maintaining temperature T_oven. The object has a specific heat c, a mass m, and an initial temperature T_0. In this problem, ignore any heat transfer by conduction or convection, and assume the oven doesn't lose any heat to the outside environment. Also assume that the time for the objects to reach a steady state is much faster than any other time scales in this problem (so we will always assume our system is in a 'steady state1) At time t, the object has temperature T(t). a) At time t, what is the net rate of heat gain by the object? b) Find the temperature of the object at a time t (You need only write out a differential equation. Only actually solve this if you are overly ambitious or have access to a table of integrals).

Explanation / Answer

(a) At time t, the net rate of heat gain by an object which is given as :

Q = h A (T - T0)

where, h = heat transfer coefficient, W/m2K

A = surface area of an object, m2

T = object temperature, K

T0 = initial temperature of object, K

Q = heat transferred, J/s

then, we get

(q / t) = h A (T - T0)

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