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Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer

A copper rod is joined to a steel rod as shown in the figure. Both rods possess equal length and identical cross sectional area. The copper rod's free end is maintained at 0^ C while the steel rod's free end is maintained at 100^ C . Determine the temperature at the junction of the two rods. The thermal conductivity of copper is 390 W m ⁻¹ ^ C⁻¹ and that of steel is 46 W m ⁻¹ ^ C⁻¹ .

Options

  1. A50.0^ C
  2. B10.6^ C
  3. C89.4^ C
  4. D11.8^ C

Correct answer

B. 10.6^ C

Step-by-step solution

Let the temperature at the junction be T . In steady state, the rate of heat flow through the copper rod is equal to the rate of heat flow through the steel rod. K_ Cu A (T - 0) L = K_ Steel A (100 - T) L Given that K_ Cu = 390 W m ⁻¹ ^ C⁻¹ and K_ Steel = 46 W m ⁻¹ ^ C⁻¹ , and the rods have equal length L and identical cross-sectional area A : 390 (T - 0) = 46 (100 - T) 390 T = 4600 - 46 T 436 T = 4600 T = 4600 436 10.55^ C Rounding to one decimal place, we get T = 10.6^ C .

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