A copper rod and an iron rod are joined end to end in a good...

A copper rod and an iron rod are joined end to end in a good thermal contact. The two rods have equal lengths and radii. The free end of the copper rod is maintained at a temperature of 109°C, and the free end of the iron rod is maintained at 0°C. (a) Determine the temperature of the interface between the two rods. (Enter your answer to at least the nearest decimal place.) (b) If each rod is 15 cm long and each has a cross-sectional area of 4.8 cm2, what quantity of energy is conducted across the combination in 30 min?

Transcript

00:01 Here is the illustration of the given situation for our limb.

00:04 So we have copper and iron rod of same length in radai, while the copper, the free end is at 190 degrees at while the free end of the iron is at zero degrees of shoes.

00:19 Now question a, want us to determine the temperature at the junction.

00:29 So since this is a heat transfer to conduction, we can determine the temperature from the formula of heat current.

00:38 So for heat transfer by conduction, heat current is equal to this.

00:44 The thermal conductivity multiplied by the cross -sectional area, multiplied by the difference of hot temperature and temperature over the length.

01:00 So in this situation, the heat current at the copper and iron are the same.

01:07 Then suppose that on the left cellucations for the copper, then we have this.

01:13 So the hot temperature minus the temperature at the junction.

01:18 So we just denote a, the areas, cross -section areas, a and the length as else, since they have the same length and radius.

01:31 So on the right side for the iron, we have this.

01:41 Then simplifying, our goal is to isolate to the left side of the equation.

01:56 We have this expanding, so grouping life terms, then salating t to the left side, we have this.

02:44 So since the t sub -h here is 190 degrees celsius, and t -c is 0 degrees celsius, then t is equal to this...

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