A copper rod and an aluminum rod of the same length and cross sectional area are attached end to endThe copper end is placed in a furnace at a constant temperature of 350 degrees CThe aluminum end is placed in an ice bath held at a constant temperature of 0.0 degrees CCalculate the temperature at the point where the two rods are joined(k 200 smC for aluminum and k380 smC for copper.)Could someone show me how to do this?
You need the formula for steady heat flow along a rodIt is: Q kA(T1 - T2)/L (1) The key point is that in the steady state the rate of heat flow along each rod is the sameSo you can equate the heat flows given by equation (1) to give an equation for the temperature at the joinSuppose the temperature of the hot end is T1, the join T2 and the cold end T3 then k(Cu) .A (T1 -T2)/L k(Al).A (T2 -T3)/L The areas and lengths cancel leaving a simple equation to solve for T2 in terms of the other two temperatures and thermal conductivities.
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