Question

A heat-conducting rod consists of an aluminum section, 0.30 m long, and a copper section, .70m long. Both sections have a cross-sectional area of 4 · 10⁻⁴m² The aluminum end of the rod is maintained at a temperature of 10°C, while the copper end is maintained at 160°C. What is the temperature at the point where the aluminum and copper sections meet? The thermal conductivity of aluminum is 205 W/m ∙ K, and of copper is 385 W/m ∙ K.
77°C


60°C


71°C


65°C


55°C

Answer 1

Thermal conductions
K= QL/ART
Aluminium T₁ = 10 + 273.15
                    T₂ = 283.15k
205 = 2.0  × 0.30/4× 10⁻⁴ × (T₂ - 283.15)
Copper
385 = Q × 0.70/4×10⁻⁴ ×(433.15 - T₂)
Where T₃ = 160 + 273.15
T₃ = 433.15K
From 2 to 3
205/385 = 0.30/0.70 × 433.15 - T₂/T₂ - 283.15
= 0.53T₂ -150.06 = 181.92 - 0.42 T₂
→ 0.95T₂ = 331.98 ⇒ T₂ = ₂349.45k
T₂ = 76.3°c
=77°c.