What is the steady state temperature of copper aluminum juction?

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  • 2 months ago

    The temperature difference between the two ends of the setup is the difference between the boiling and freezing points of water.  If we take these to be 100° C and 0° C, then that difference is 100° C, which is the same as 100° K for a difference.

    One way of working the problem would be to solve for the power, P, flowing through the rods, which, for a physics question, we assume flows without loss through the rods, that is, no radiation or convection loss.  Then we could use the power going through the copper rod to calculate the temperature drop from 100 over 1 meter.

    However, we're only interested in temperature, so an easier way would be to realize that the temperature drops across the rods will be proportional to the thermal resistances, which are the reciprocals of the thermal conductivities.  That is

    (drop across Copper) : (drop across Aluminum) : (drop across Brass)

    =

    (1/400) : (1/200) : (1/109) =

    .0025 : .005 : .0092

    The total drop across all 3 bars is 100, so we need 3 numbers in that ratio which add to 100.

    .0025 k + .0050 k + .0092 k = 100

    25 k + 50 k + 92 k = 10^6

    167 k = 10^6

    Then solve for k, and the drop of temperature over the copper bar will be .0025 k.  Subtract that from 100, and you'll have the temperature at the copper-aluminum junction.

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