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What is the temperature of steel-copper ...

What is the temperature of steel-copper junction in the steady state of the system shown in fig. Length of the steel rod = 30.0 cm, length of the copper rod = 20.0 cm, temperature of the furnace = `300^(@)C`, temperature of cold end `=0^(@)C` . The area of cross-section of the steel rod is twice that of the copper rod. thermal conductivity of steel = `50 .2 Js^(-1) m^(-1) .^(@)C^(-1)` and of copper = `358 Js^(-1) m^(-1) .^(@)C^(-1)`.

Text Solution

Verified by Experts

`K_1 = 50.2 Js^(-1) m^(-1) ""^@C^(-1)`
`K_2 = 585 Js^(-1) m^(-1) C^(-1)`
`A_1 = 3A_2`
Let T be the temperature of the junction. Then, in the steady state of the system, Rate of inflow of heat = Rate of outflow of heat
` rArr (K_1A_1 (200 - T))/(x_1) = (K_2A_2 (T-0))/(x_2)`
`(200-T)/(T) =k_2/K_1 xx A_2/A_1 xx x_1/x_2`
` = (585)/(50.2) xx 1/3 xx 20/15`
` T = 45.5^@C`
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