Two rods, one of copper and the other of steel, each of cross-sectional area , are…

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

Two rods, one of copper and the other of steel, each of cross-sectional area

5.0\,\text{cm}^2

, are brazed together end-to-end so that they form a composite rod of total length

0.60\,\text{m}

(the copper section being

0.20\,\text{m}

long and the steel section

0.40\,\text{m}

long). The free end of the copper section is kept at

100\,^{\circ}\mathrm C

while the free end of the steel section is maintained at

40\,^{\circ}\mathrm C

until steady state is reached. Take thermal conductivities as

k_{\text{Cu}} = 400\,\text{W m}^{-1}\text{K}^{-1}

and

k_{\text{steel}} = 50\,\text{W m}^{-1}\text{K}^{-1}

. (a) Derive an expression for the temperature

T

at the junction of the two rods in terms of the given lengths, thermal conductivities, and the temperatures at the free ends. (b) Hence calculate the numerical value of

T

under the given conditions. (c) Determine the common steady rate of heat flow through the composite rod.

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