Question

The temperature of an electronic oven is 167.3°C. The temperature at the outer surface of the oven in the kitchen is 48.8 °C. The oven (surface area = 1.7 m2) is insulated with material that has a thickness of 0.02 m and a thermal conductivity of 0.04 J/(s m C°). How much energy in Joules will be used to operate the oven over 3 hours?

Answer 1

Question#18832

The temperature of an electronic oven is 167.3 C. The temperature at the outer surface of the oven in the kitchen is 48.8 C. The oven (surface area = 1.7 m²) is insulated with material that has a thickness of 0.02 m and a thermal conductivity of 0.04 J/(s m C). How much energy in Joules will be used to operate the oven over 3 hours?

Solution:

Let:

$$t_0 = 48.8 \, {}^{\circ}\mathrm{C}$$ $$t_1 = 167.3 \, {}^{\circ}\mathrm{C}$$ $$S = 1.7 \, \mathrm{m}^2$$ $$d = 0.02 \, \mathrm{m}$$ $$k = 0.04 \, \mathrm{J}/\mathrm{s} \, \mathrm{m}{}^{\circ}\mathrm{C}$$ $$T = 3 \, \mathrm{hours} = 10800 \, \mathrm{sec}$$

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Q-?

Q = qT, were q - the heat flux, T - time

According to the Fourier's law (the law of heat conduction):

$$q = k \frac{S \Delta t}{d}$$ $$\Delta t = t_1 - t_0$$ $$q = k \frac{S(t_1 - t_0)}{d}$$ $$Q = k T \frac{S(t_1 - t_0)}{d}$$ $$Q = 0.04 * 10800 * \frac{1.7(167.3 - 48.8)}{0.02} = 2559600 \, \mathrm{J}$$

Answer: 259600 J (256.6 KJ)