Concepts Of Physics MCQ Edition [Volume 2]
- Exam
- Concepts Of Physics MCQ Edition [Volume 2]
- Subject
- Physics
- Chapter
- Heat Transfer
Concepts Of Physics MCQ Edition [Volume 2] · Physics · Heat Transfer
A copper rod is joined to a steel rod as shown in the figure. Both...
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^{}^{{}^{\circ}} C while the steel rod's free end is maintained at 100^{}^{{}^{\circ}} C. Determine the temperature at the junction of the two rods. The thermal conductivity of copper is 390 \text{ W m}^{-1} ^{}^{{}^{\circ}} C^{-1} and that of steel is 46 \text{ W m}^{-1} ^{}^{{}^{\circ}} C^{-1}.
Options
- A50.0^{}^{{}^{\circ}} C
- B10.6^{}^{{}^{\circ}} C
- C89.4^{}^{{}^{\circ}} C
- D11.8^{}^{{}^{\circ}} C
Correct answer
B. 10.6^{}^{{}^{\circ}} C
Step-by-step solution
Let the temperature at the junction be .
In steady state, the rate of heat flow through the copper rod is equal to the rate of heat flow through the steel rod.
Given that K_{Cu} = 390 \text{ W m}^{-1} ^{}^{{}^{\circ}} C^{-1} and K_{Steel} = 46 \text{ W m}^{-1} ^{}^{{}^{\circ}} C^{-1}, and the rods have equal length and identical cross-sectional area :
T = \dfrac{4600}{436} \approx 10.55^{}^{{}^{\circ}} C
Rounding to one decimal place, we get T = 10.6^{}^{{}^{\circ}} C.
In steady state, the rate of heat flow through the copper rod is equal to the rate of heat flow through the steel rod.
Given that K_{Cu} = 390 \text{ W m}^{-1} ^{}^{{}^{\circ}} C^{-1} and K_{Steel} = 46 \text{ W m}^{-1} ^{}^{{}^{\circ}} C^{-1}, and the rods have equal length and identical cross-sectional area :
T = \dfrac{4600}{436} \approx 10.55^{}^{{}^{\circ}} C
Rounding to one decimal place, we get T = 10.6^{}^{{}^{\circ}} C.