Finding thermal conductivity of an insulated metal bar

In summary, the heat conducted by an insulated metal rod with a length of 60.0cm and a cross-sectional area of 1.40cm2 melts a mass of 7.15g of ice in 15.0min. By converting to SI units and using the equation (heat/time) = k(A)(ΔT/L), we can find the thermal conductivity K of the metal to be 114 W/m*K.
  • #1
reed2100
49
1

Homework Statement



One end of an insulated metal rod is maintained at 100∘C and the other end is maintained at 0.00 ∘C by an ice–water mixture. The rod has a length of 60.0cm and a cross-sectional area of 1.40cm2 . The heat conducted by the rod melts a mass of 7.15g of ice in a time of 15.0min .
Find the thermal conductivity K of the metal.

Homework Equations



(Heat/time) = k(A)(ΔT/L)
H(fusion) for water = 334 KJ/kg*K = 334000 J/kg

The Attempt at a Solution



Converting to SI units -> L=.6 m, A= .014 m^2, m(ice) = .00715 kg, time= 900s

Q=heat/time, so heat = .00715 kg(334000 J/kg) = 2388 J, Q = 2388J/900s = 2.6533 J/s = 2.653W

So, 2.653 W = k(.014 m^2)(100°C/.6m)

2.653 W / ( .014 m^2 ) *.6m / 100 C ≈ 1.14 W/m*C OR 1.14W/m*K since K or C can be used interchangeably here.

So, my answer kept coming up as 1.14, yet the correct answer was 114 W/m*K.

I am confused as to why I'm getting the correct answer in a sense but with my order of magnitued off. It makes me wonder if I'm doing my math correctly or I made a careless mistake somewhere. Any and all help/advice will be greatly appreciatied.
 
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  • #2
reed2100 said:
A= .014 m^2
Try that one again.
 
  • #3
Oh, I completely forgot to divide by 100 twice. I'm getting the right answer now, thanks!
 

Related to Finding thermal conductivity of an insulated metal bar

1. What is thermal conductivity?

Thermal conductivity is the measure of a material's ability to conduct heat. It is a property that determines how quickly heat can pass through a material.

2. Why is it important to find the thermal conductivity of an insulated metal bar?

Knowing the thermal conductivity of an insulated metal bar is important for understanding how the material will respond to changes in temperature. It is also crucial for designing and optimizing insulation systems to maintain desired temperatures and reduce energy consumption.

3. How do you measure the thermal conductivity of an insulated metal bar?

The thermal conductivity of an insulated metal bar can be measured using a device called a thermal conductivity meter or by conducting a heat transfer experiment. The experiment involves measuring the temperature change over time of the metal bar with and without insulation, and using this data to calculate the thermal conductivity.

4. What factors can affect the thermal conductivity of an insulated metal bar?

The thermal conductivity of an insulated metal bar can be affected by factors such as the type of metal, the insulation material and thickness, the temperature difference between the two sides of the bar, and any external factors such as air flow or humidity.

5. Can the thermal conductivity of an insulated metal bar change over time?

Yes, the thermal conductivity of an insulated metal bar can change over time due to factors such as aging, degradation of insulation material, and changes in environmental conditions. It is important to regularly check the thermal conductivity to ensure optimal performance of the insulated metal bar.

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