Heat Flowing Through A Sectioned Rod HELP

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In summary, a long rod, insulated to prevent heat loss, is in thermal contact with boiling water and an ice-water mixture. It consists of a copper section and a steel section, both with cross-sectional areas of 4.00. The temperature of the junction is 65.0 after reaching steady state. Using the equation H=kAdT/L, with kcopper=385 and ksteel=50.2, the heat transfer from the boiling water to the ice-water mixture is approximately 21.56 watts. The error in the initial attempt was squaring the area, which should have been multiplied by 10^-4 to convert from cm squared to m squared.
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tizzful
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Homework Statement



A long rod, insulated to prevent heat loss along its sides, is in perfect thermal contact with boiling water (at atmospheric pressure) at one end and with an ice-water mixture at the other. The rod consists of a 1.00 section of copper (with one end in the boiling water) joined end-to-end to a length of steel (with one end in the ice water). Both sections of the rod have cross-sectional areas of 4.00 . The temperature of the copper-steel junction is 65.0 after a steady state has been reached.
How much heat per second flows from the boiling water to the ice-water mixture?
Express your answer in watts

Homework Equations



H=kAdT/L
kcopper=385
ksteel=50.2

The Attempt at a Solution



Hcopper=Hsteel
Hcopper=385*0.04^2*35
= 21.56W
There's something wrong with this answer.. Can someone please help me?
Thank you!
 
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  • #2
Hi tizzful,

In your expression you have squared 0.04 (which is (area/length) in meters); since they gave the area I don't believe that number should be squared.
 
  • #3
Hello, yes I realized afterwards that its in cm squared and I need it in meters squared and therefore had to multiply it by 10^-4. Thank you
 

1. How does heat flow through a sectioned rod?

The rate at which heat flows through a sectioned rod depends on several factors, including the temperature difference between the two ends of the rod, the material of the rod, and the cross-sectional area of the rod. Heat always flows from areas of high temperature to areas of low temperature, so in a sectioned rod, heat will flow from the hotter section to the cooler section.

2. What is the equation for calculating heat flow through a sectioned rod?

The equation for heat flow through a sectioned rod is Q = kA (T1 - T2)/L, where Q is the heat flow, k is the thermal conductivity of the material, A is the cross-sectional area, T1 and T2 are the temperatures at the two ends of the rod, and L is the length of the rod. This equation is known as Fourier's law of heat conduction.

3. How does the material of the rod affect heat flow?

The material of the rod plays a significant role in determining the rate of heat flow through a sectioned rod. Materials with high thermal conductivity, such as metals, allow heat to flow more easily than materials with lower thermal conductivity, such as wood. This is because materials with high thermal conductivity have a higher ability to transfer heat energy.

4. What is the importance of cross-sectional area in heat flow through a sectioned rod?

The cross-sectional area of a sectioned rod affects the rate of heat flow because it determines the amount of surface area available for heat to transfer through. A larger cross-sectional area means there is more surface area for heat to flow through, resulting in a higher rate of heat flow. This is why thicker rods typically have a higher heat flow than thinner rods.

5. How can heat flow through a sectioned rod be controlled?

Heat flow through a sectioned rod can be controlled in several ways. One way is by changing the temperature difference between the two ends of the rod. A larger temperature difference will result in a higher rate of heat flow. Additionally, the material and cross-sectional area of the rod can also be altered to control the rate of heat flow. Insulating materials can also be used to reduce heat flow through a sectioned rod.

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