Question

Figure (28-E2) shows a copper rod joined to a steel rod. The rods have equal length and equal cross sectional area. The free end of the copper rod is kept at 0°C and that of the steel rod is kept at 100°C. Find the temperature at the junction of the rods. Conductivity of copper = 390 W m⁻¹°C⁻¹ and that if steel = 46 W m⁻¹°C⁻¹.

Answer 1

Rods are connected in series, so the rate of flow of heat is same.

q₁ = q₂

Rate of flow of heat is given by
$q=\frac{dQ}{dt}=\frac{\mathrm{Temperature}\mathrm{difference}}{\mathrm{Thermal}\mathrm{resistance}}$

As q₁ = q₂,
$$\begin{gathered} \Rightarrow \frac{T-0}{R_{\mathrm{cu}}}=\frac{100-T}{R_{\mathrm{S}}} \\ A{K}_1\left(\frac{T-0}{l}\right)=\left(\frac{100-T}{l}\right)K_{2}A \\ \Rightarrow 390\mathrm{T}=\left(100-\mathrm{T}\right)46 \\ \Rightarrow \mathrm{T}=10.6°\mathrm{C} \end{gathered}$$