What is the correct method for solving thermal conductivity in this problem?

In summary, a metal rod with one end at 100 degrees C and the other end at 0 degrees C, with a length of 60 cm and cross-sectional area of 1.25 cm^2, conducts enough heat to melt 8.50 g of ice in 10.0 min. Taking into account a 30% heat loss to the surroundings, the thermal conductivity of the metal is 0.777 cal/cm.s.C.
  • #1
Zhao_1911
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Homework Statement


One end of a metal rod is maintained at 100 degrees C, and the other end is maintained at 0 degrees C by an ice-water mixture. The rod is 60 cm long and has a cross-sectional area of 1.25 cm^2. The heat conducted by the rod melts 8.50 g of ice in 10.0 min. Find the thermal conductivity of the metal if 30% of heat is lost to the surroundings.


Homework Equations


(Q/t) = mLf/t
where (Q/t) is the heat flow, Lf is the latent heat of fusion

(Q/t) = KA(delta T)/L
where K is the thermal conductivity of the metal, A is the area, delta T is the temperature difference, and L is the length.


The Attempt at a Solution


First, I solved the heat flow of the metal using the mass of the melted ice and the time it took to melt that amount of ice;

(Q/t)= [8.5g(80cal/g)x.70]/600s = 119/150 cal/s

Then I solved the K of the metal;

119/150 cal/s = [K(1.25 cm^2)(100C-0C)]/60 cm
K = 0.381 cal/cm.s.C

BUT THEN..
I saw a solution of my classmate that used something like this;

(Q/t)={[8.5g(80cal/g)]/.70}/600s = 34/21 cal/s

so his K is about 0.777 cal/cm.s.C

that's where I'm confused. Should I divide or multiply the .70?
 
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  • #2
Your friend is correct.
 

What is thermal conductivity and why is it important?

Thermal conductivity is a measure of a material's ability to conduct heat. It is important because it affects the rate of heat transfer through a material, which is essential for many engineering and scientific applications.

How is thermal conductivity measured and what units is it expressed in?

Thermal conductivity is typically measured using a device called a heat flow meter or a thermal conductivity meter. It is expressed in units of watts per meter-kelvin (W/mK) in the International System of Units (SI).

What factors affect thermal conductivity?

The thermal conductivity of a material is affected by several factors, including its chemical composition, density, temperature, and the presence of impurities or defects. Generally, materials with higher thermal conductivity have stronger atomic bonds and are more rigid, while materials with lower thermal conductivity have looser atomic bonds and are more flexible.

What are some common materials with high and low thermal conductivity?

Metals, such as copper and aluminum, have high thermal conductivity due to their strong atomic bonds and free-moving electrons. Insulating materials, such as wool and Styrofoam, have low thermal conductivity due to their loosely packed and lightweight structures. However, there are exceptions to these trends, so it is important to check the thermal conductivity values of specific materials.

How is thermal conductivity used in real-world applications?

Thermal conductivity is used in a wide range of applications, including building insulation, electronics cooling, and energy production. It is also important in the design of materials for various industries, such as aerospace and automotive. Additionally, understanding thermal conductivity can help in predicting and preventing heat-related problems in machinery and equipment.

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