TS EAMCET · Physics · Thermal Properties of Matter
An aluminium rod of length \(1 \mathrm{~m}\) and a steel rod of length \(2 \mathrm{~m}\) both having same cross-sectional area, are soldered together end-to-end. The thermal conductivity of aluminium rod and steel rod is \(200 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}\) and \(50 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}\) respectively. The temperatures of the free ends are maintained at \(300 \mathrm{~K}\) and \(500 \mathrm{~K}\). What is the temperature of the junction?
- A \(322 \mathrm{~K}\)
- B \(350 \mathrm{~K}\)
- C \(367 \mathrm{~K}\)
- D \(400 \mathrm{~K}\)
Answer & Solution
Correct Answer
(A) \(322 \mathrm{~K}\)
Step-by-step Solution
Detailed explanation
Let junction temperature is \(T K\), then in steady state heat flow rate is same through both rods. So, using, \(\frac{Q}{t}=\frac{k A\left(T_2-T_1\right)}{l}\), we have, \[ \frac{Q}{t}=\frac{k_s A_s(500-T)}{2}=\frac{k_{\mathrm{Al}} A_{\mathrm{Al}}(T-300)}{1} \] As areas of both…
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