Question

As a mechanical engineer, you are given two uniform metal bars A and B, made from different metals, to determine their thermal conductivities. You measure the bars to have length 40.0 cm and uniform cross-sectional area 2.30 cm^2. After conducting a thermal conductivity experiment, you find that the composite bar remains at 62.4 °C with ice still in the ice-water mixture. What can you conclude about the thermal conductivities of bars A and B?

Answer 1

The uniform bars A and B in the described experiment suggest equal thermal conductivities due to the same temperature being maintained at the contact with ice. To firmly conclude, additional measurements of heat flux and temperature gradients would be necessary.

Step-by-step explanation:

The question pertains to the experimental determination of thermal conductivity for two uniform metal bars, given fixed dimensions and a constant temperature setup with an ice-water mixture. In the provided scenario, if both bars remain at the same temperature of 62.4 °C while in contact with ice, which is at 0 °C, we could assume that both bars have the same thermal conductivity. This is because, under steady-state conditions and assuming no heat loss to the surroundings, the temperature at the junction will be the same if both conductivities are equal. To formally conclude the thermal conductivities of bars A and B, we would need to consider the heat flux through both bars given their material properties and determine if there's a temperature gradient along the length of each bar. If no such gradient exists, it supports the claim of equal conductivities. However, for a definitive conclusion, we would require specific values of the heat flux and potential temperature gradients, which are not provided here.