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Problem 56 is about two roads, one made of brass, the other made of copper.
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Their lengths are given in meters.
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The brass end is kept in boiling water at 100 degrees celsius, while the copper end is kept in a mixture of ice and water at 0 degrees celsius.
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Both roads are joined at a point.
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P and our task our first task is to find the temperature at p.
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The physics here is to know that the rate at which heat is transferred from the boiling water is the same rate at which it is transferred through the brass and copper.
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So we put that in mathematical language.
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The weight of heat transfer in the boiling water equals the rate of heat transfer to the brass, which is given by the conductivity of brass, the cross -session of brass, times the change in temperature.
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And the temperature change for the brass is from 100 to the temperature at p, all divided by the length of brass.
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The brass and we're giving.
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So this is the weight at which it is transferred to our brass and that should be equal to the weight at which it is transferred to the copper road.
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For copper the temperature difference is from p to zero that is p minus zero the temperature at p minus zero over the length of grass.
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So so that is the physics essentially, the rate at which heat is transferred through brass equals rate at which it is transferred through copper.
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Since the cross sessions are the same, we are told that the cross sessions are equal in square meters, or it is in square meters.
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So it comes out.
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And so we only have to equate this two and make tp the subject...