A single piece of graphite will have a significantly differe

A single piece of graphite will have a significantly different thermal conductivity depending on the direction of heat flow through the material due to its atomic structure. Graphite hasa thermal conductivity of about W m *K 1 In one direction and about(l600 W m 5K 1 in the perpendicular direction Based on the schematic diagram (not drawn to scale) of a 1 cm x 1cm x 1cm cube of graphite assign a thermal conductivity (1000 Of 5 W m 1 K\') to each direction based on the temperature gradient Explain your reasoning for each assignment (the conduction equation would be a good start)

Solution

from the conduction equation:

Dq / Dt = k DT / Dx

consider directio along y axis:
DT = 100 - 72 = 28
Dx = 1 cm = 0.01m
Let Dq / Dt = L (constant)
Then, k1 = L * Dx / DT = L * (0.01 / 28) = 0.0003571 * L -- (1)

consider directioa long x direction:
DT = 100 - 96 = 4
Dx = 1 cm = 0.01m
Let Dq / Dt = L (constant)
Then, k2 = L * Dx / DT = L * (0.01 / 4) = 0.0025 * L -- (2)

a and b) As the conduction equation clearly states, Temperature gradient DT /Dx is inversly proporional to k. So higher the gradient, lower is the thermal conductivity.
K for case 1 = 5 W m-1 k-1
K for case 2 = 1000 W m-1 k-1