A square steel bar of side length w = 0.11 m has a thermal conductivity of k = 1

Question

A square steel bar of side length w = 0.11 m has a thermal conductivity of k = 152 J/(s middot m middot degree C) and is L- 2.4 m long. Once end is placed under a candle so that the temperature is T_1 = 84 degree C while the other end rests on a block of ice so that the temperature is a constant T_2. Input an expression for the heat transferred to the cold end of the bar as a function of time, using A = w^2 as the cross-sectional area of the bar. How much energy, in joules, was conducted in 1 hour, assuming T_2 = 0 degree C? Input an expression for the mass of the water melted in 1 hour using Q_1 from above and L_f the latent heat of fusion.

Explanation / Answer

Given

the steel bar of w = 0.11m, l= 2.4 m

one end is at temperature T1 = 84 0C, other end at T2 = 0 0C

T1> T2

and coefficient of thermal conductivity is k =15.2 J / s.m 0C

we know that the heat energy will be transfered in solids from one point to the other point by means of condution

   the rate of heat transfer is dQ/dt is proportional to Area and change in temperature

also inversly proportional the the length

   so dQ/dt = k *A*(T1-T2)/L

   dQ/dt = k*w^2(T1-T2)/L

      

this is the expression for the rate of heat transfer through the steel bar

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