Question

Determine the quantity of heat conducted in thirty minutes through an iron plate 2.0 cm thick and 0.10m^2 in area if the temperatures of the two sides are 0 Degrees Celsius and 20 Degrees Celsius. The coefficient of thermal conductivity of iron is 50.4 J/smC.

(A) 9.1 X 10^6J

(B) 2.3 X 10^6J

(C) 4.1 X 10^6J

(D) 3.3 X 10^6J

Answer 1

Let:

$$S = 0.1 \, \mathrm{m}^2$$ $$d = 2.0 \, \mathrm{cm} = 0.02 \, \mathrm{m}$$ $$T1 = 0{}^\circ \mathrm{C}$$ $$T2 = 20{}^\circ \mathrm{C}$$ $$k = 50.4 \, \mathrm{J} / \mathrm{sm}{}^\circ \mathrm{C}$$ $$t = 30 \, \mathrm{min} = 1800 \, \mathrm{second}$$ $$Q = ?$$

The quantity of heat is:

$$Q = t \cdot k \frac{S \Delta T}{d} \quad \text{(Fourier's law)}$$ $$\Delta T = T2 - T1 = 20{}^\circ$$

Enter a data:

$$Q = 1800 \cdot 50.4 \frac{0.1 \cdot 20}{0.02} = 9072000 \, \mathrm{J} = 9.1 \cdot 10^6 \, \mathrm{J}$$

Answer: "A"