Solve Physics Problem: Heat Conducted Through 2 Rods

In summary, two rods made of aluminum and copper with cross-sectional areas of 4.0 x 10^-4 m^2 and lengths of 0.040m are joined together, with one end of the aluminum rod at 302 degrees Celsius and the other end of the copper rod at 25 degrees Celsius. The problem asks for the amount of heat conducted through the unit in 2 seconds, and to solve it, one must use the thermal conductivity of each material and the Fourier law of heat conduction. The concept of thermal resistance is also useful in this case, as the resistances of the two rods can be summed to find the total resistance.
  • #1
Mathwizard6254
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Two rods, one of aluminum and the other of copper, are joined end to end. The cross-sectional area of each is 4.0 x 10^-4 m^2, and the length of each is 0.040m. The free end of the aluminum rod is kept at 302 degrees Celsius, while the free end of the copper rod is kept at 25 degrees Celsius. The loss of heat through the sides of the rods may be ignored. How much heat is conducted through the unit in 2 seconds? Please show the work done in solving this problem. THank you very much!
 
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  • #2
You should show what work you have done so that people can help you understand it better. To solve this problem, you'll need to look up the thermal conductivity of each material involved. The following equation defines the rate of conduction heat transfer through a barrier (aka Fourier law of heat conduction - I think my notation is standard or at least self-explanatory; I hope you can follow it):

[tex] q = \frac{Q}{t} = kA\frac{T_2 - T_1}{L} [/tex]

When dealing with a series of barriers as in this case, it is useful to consider the concept of a thermal resistance (analagous to electrical resistance):

[tex] R_{th} = \frac{L}{kA} [/tex]

Then you can sum the resistances that are in series to find:

[tex] \frac{Q}{t} = \frac{\Delta T}{\Sigma_i{R_{th, i}}} [/tex]

(For this problem, you'll want to solve for Q.)
 
  • #3


To solve this physics problem, we will use the equation for heat conduction:

Q = kAΔT / L

Where:
Q = heat conducted
k = thermal conductivity constant (depends on the material)
A = cross-sectional area
ΔT = change in temperature
L = length

First, we need to find the thermal conductivity constant for aluminum and copper. According to the table of thermal conductivity constants, the thermal conductivity constant for aluminum is 205 W/mK and for copper is 385 W/mK.

Next, we can calculate the change in temperature (ΔT) for each rod:

ΔT(aluminum) = 302°C - 25°C = 277°C
ΔT(copper) = 302°C - 25°C = 277°C

Now, we can plug in the values into the equation:

Q(aluminum) = (205 W/mK)(4.0 x 10^-4 m^2)(277°C) / 0.040m = 569.25 W

Q(copper) = (385 W/mK)(4.0 x 10^-4 m^2)(277°C) / 0.040m = 1058.5 W

Since the two rods are joined end to end, the heat conducted through both rods will be the same. Therefore, we can add the two values together to get the total heat conducted:

Q = 569.25 W + 1058.5 W = 1627.75 W

Finally, we need to convert the unit of time from seconds to hours, since the thermal conductivity constants are given in W/mK. There are 3600 seconds in 1 hour, so we can calculate the heat conducted in 2 seconds as:

Q = (1627.75 W)(2 s) / (3600 s/h) = 0.904 W

Therefore, in 2 seconds, 0.904 watts of heat will be conducted through the two rods.
 

What is heat conduction?

Heat conduction is the transfer of thermal energy between two bodies that are in direct contact with each other. In this process, the hotter body transfers heat to the colder body, until they reach thermal equilibrium.

How does heat conduction occur through two rods?

In the case of two rods, heat conduction occurs through direct molecular contact. The atoms in the hotter rod vibrate faster and collide with the atoms in the colder rod, transferring energy and increasing their temperature. This process continues until both rods reach the same temperature.

What factors affect the rate of heat conduction through two rods?

The rate of heat conduction through two rods depends on several factors, including the material of the rods, their cross-sectional area, their length, and the temperature difference between the two rods. These factors affect the speed at which heat can be transferred between the rods.

How can the rate of heat conduction through two rods be calculated?

The rate of heat conduction through two rods can be calculated using the formula Q/t = kAΔT/Δx, where Q/t is the heat flow rate, k is the thermal conductivity of the material, A is the cross-sectional area, ΔT is the temperature difference, and Δx is the distance between the two rods.

How can heat conduction through two rods be applied in real-life situations?

Heat conduction through two rods is a fundamental concept in the field of thermodynamics and is applicable in many real-life situations. Some examples include the transfer of heat through a metal pot on a stove, the cooling of a computer processor through a heat sink, and the transmission of heat in building insulation.

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