Question

The block in the drawing has dimensions L0×2L0×3L0,where L0 =0.5 m. The block has a thermal conductivity of 200 J/(s·m·C˚). In drawings A, B, and C, heat is conducted through the block in three different directions; in each case the temperature of the warmer surface is 37 ˚C and that of the cooler surface is 7 ˚C Determine the heat that flows in 4 s for each case.

Answer 1

Answer:

$Q_p=18000\ J$

$Q_o=8000\ J$

$Q_g=72000\ J$

Explanation:

Given:

• Length of block, $l=3L_o=3\times 0.5=1.5\ m$

• Breadth of block, $b=L_o=0.5\ m$

• height of block, $h=2L_o=2\times 0.5=1\ m$

• Thermal conductivity of the block, $k=200\ W.m.^{\circ}C$

• Temperature on the hotter side, $T_H=37^{\circ}C$

• temperature on the cooler side, $T_L=7^{\circ}C$

• time for which the heat flows, $t=4\ s$

REFER THE ATTACHED IMAGE FOR THE REFERENCE

The rate of heat flow using Fourier's law of conduction is given as:

$\frac{Q}{t}=k.A.\frac{dT}{dx}$

Now the amount heat flow perpendicular to the pink surface:

$\frac{Q_p}{4}=200\times (0.5\times 1.5).\frac{30}{1}$

$Q_p=18000\ J$

Now the amount heat flow perpendicular to the orange surface:

$\frac{Q_o}{4}=200\times (0.5\times 1).\frac{30}{1.5}$

$Q_o=8000\ J$

Now the amount heat flow perpendicular to the green surface:

$\frac{Q_g}{4}=200\times (1.5\times 1).\frac{30}{0.5}$

$Q_g=72000\ J$