# Conduction between a steel/copper cylinder.

• jj5959
In summary, the problem involves calculating the amount of heat that will flow through two cylinders, one made of steel and the other made of copper, when their free ends are maintained at different temperatures. Using the given dimensions and thermal conductivities for each material, the heat transfer equation is used to solve for the temperature in the middle of the cylinders and then calculate the heat flow. However, there is a discrepancy between the calculated result and the given answer.
jj5959

## Homework Statement

A steel cylinder of radius 7.0 cm and length 4.0 cm is placed in end-to-end thermal contact with a copper cylinder of the same dimensions. If the free ends of the two cylinders are maintained at constant temperatures of 85°C (steel) and 20°C (copper), how much heat will flow through the cylinders in 19 min?

## Homework Equations

Q = (kAtdeltaT)/L

Q=heat
k for steel=66.9
k for copper=395
A=area
t=time
T=temperature
L=length

## The Attempt at a Solution

x=temperature in the middle of the cylinders

I set heat transferred through the steel part of the cylinder equal to the heat transferred through the copper part of the cylinder.

(66.9)(85-x) = (395)(x-20)
x=29.4

then using that value, i solved for Q.

Q=((66.9)(.0154)(85-29.4)(1140))/.04
so Q=1.6E6 J

BUT the answer is Q=1.17E6 J
where'd i go wrong?

Q=1.17E6 J should be right. Perhaps the answer key is wrong?

Your attempt at a solution is correct, but the difference in the final answer is due to rounding errors. When solving for x, you get x=29.4118, but in your calculation for Q, you used x=29.4. This small difference in x leads to a difference in the final answer. To get the correct answer, you can use the more precise value of x (29.4118) in your calculation for Q.

## 1. How does conduction occur between a steel/copper cylinder?

Conduction is the transfer of heat or electricity through a material, and in the case of a steel/copper cylinder, it occurs through the movement of free electrons within the material. When heat is applied to one end of the cylinder, the molecules in that area gain kinetic energy and vibrate, causing neighboring molecules to vibrate and transfer the energy along the cylinder. This process continues until the entire cylinder reaches an equilibrium temperature.

## 2. What factors affect the rate of conduction between a steel/copper cylinder?

The rate of conduction between a steel/copper cylinder is affected by several factors, including the temperature difference between the two ends of the cylinder, the material's thermal conductivity, and the cross-sectional area of the cylinder. A higher temperature difference, higher thermal conductivity, and larger cross-sectional area will result in a faster rate of conduction.

## 3. How does the length of a steel/copper cylinder affect conduction?

The length of a steel/copper cylinder can affect conduction by increasing the distance that heat must travel. The longer the cylinder, the more molecules there are that must transfer energy, resulting in a slower rate of conduction. However, the impact of length may be minimal compared to other factors such as temperature difference and material properties.

## 4. What is the difference between thermal conduction and electrical conduction in a steel/copper cylinder?

Thermal conduction and electrical conduction are both forms of conduction that occur in a steel/copper cylinder, but they involve different types of energy transfer. Thermal conduction involves the transfer of heat energy, while electrical conduction involves the transfer of electrical energy. The mechanisms of conduction are similar, but the driving force and resulting effects are different.

## 5. Can conduction occur between a steel/copper cylinder and other materials?

Yes, conduction can occur between a steel/copper cylinder and other materials. As long as there is physical contact between the materials, heat or electricity can transfer through conduction. The rate of conduction may vary depending on the materials' properties and the contact between them. For example, conduction may occur more quickly between two metals compared to between a metal and an insulator.

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