Question

consider a metal rod that has 10 w of heat conduction between its two ends, which are maintained at temperatures of 200 k and 400 k. if we lower the temperature of both ends by 100 k, what is the new rate of heat conduction along the rod?

Answer 1

The theories behind Fourier's Law of Heat Conduction are relevant to this query. "15 W" is the new rate of heat conduction.

Calculation:

The rate of heat conduction is determined by Fourier's Law of Heat

Conduction using the following formula:

Q = Rate of heat conduction = 10 W K = Thermal conductivity of the rod's material where Q = -kA T/X

A is the rod's cross-sectional area.

T = temperature change equals 400 K - 200 K = 200 K.

x = rod length

In light of this, 10w/200k=-kA/X -kA/X=0.05w/k.

Now, the temperature difference will only change for the altered temperature:

ΔT' = 500 K - 200 K = 300 K

Therefore,\sQ¹=-kA/ΔX(ΔT)

Q¹=(0.05W/K)(300)K

Q' = 15 W

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