Final answer:
To calculate the heat-conduction rate through the steel rod and the aluminum rod at the joint, use the formula: Heat-conduction rate = (thermal conductivity) * (cross-sectional area) * (temperature difference). The heat-conduction rates through both rods should be equal at the joint.
Step-by-step explanation:
To calculate the heat-conduction rate through the steel rod and the aluminum rod at the joint, we need to use the formula:
Heat-conduction rate = (thermal conductivity) * (cross-sectional area) * (temperature difference)
For the steel rod:
Heat-conduction rate = (80 W/m °C) * (7.85 × 10^−5 m²) * (100 °C – T)
For the aluminum rod:
Heat-conduction rate = (220 W/m °C) * (7.85 × 10^−5 m²) * (T – 50 °C)
Since the rods are welded end to end, the heat-conduction rates through both rods should be equal at the joint.