Thermal Conductivity of a Metal Rod

• Koshi
In summary, the conversation discusses a problem involving an insulated metal rod with one end maintained at 100^\circ C and the other end at 0.00 ^\circ {\rm C}. The rod has a length of 75.0 cm and a cross-sectional area of 1.40 cm^2, and is used to melt 7.85 g of ice in 15.0 min. The goal is to find the thermal conductivity k of the metal. The formula for heat transfer is used, substituting dQ/dt for H and using the equation Q=mL to find the heat transformation. The resulting value for k is 0.0022796947 w/(m*K), which may be incorrect due to a
Koshi

Homework Statement

One end of an insulated metal rod is maintained at 100^\circ C and the other end is maintained at 0.00 ^\circ {\rm C} by an ice–water mixture. The rod has a length of 75.0 cm and a cross-sectional area of 1.40 cm^2. The heat conducted by the rod melts a mass of 7.85 g of ice in a time of 15.0 min. Find the thermal conductivity k of the metal.

Homework Equations

H=dQ/dt=kA(T2-T1)/L

The Attempt at a Solution

I tried to solve for k using the formula for heat transfer and since H was not given, I substituted it with dQ/dt. Then in stead of dQ I used the equation for heat transformation Q=mL where m=mass of ice melted and L=333kj/kg which is the heat of fusion for water, if I'm not mistaken. I put everything in SI units and solved but I got the wrong answer. Did I make a wrong assumption somewhere?

That all sounds good but the devil is in the details. What answer did you get?

I got the answer 0.0022796947 w/(m*K)

is there anyone else who can help me find out where I went wrong?

Please show one's work, particularly, the value obtained for heat flux. If one is off by 4-orders of magnitude, look at the value for cross-sectional area given in cm2 and make sure it is properly converted to m2.

I obtain a value on the order of the thermal conductivity of a metal. Thermal conductivity of Al is about 200 W/m-K, and that of Cu is about 385 W/m-K.

Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/tables/thrcn.html#c1

1. What is thermal conductivity?

Thermal conductivity is a measure of how well a material can transfer heat. It describes the rate at which heat energy is conducted through a material, such as a metal rod.

2. How is thermal conductivity measured?

Thermal conductivity is typically measured in watts per meter-kelvin (W/mK) or British thermal units per hour-foot-degree Fahrenheit (BTU/hr-ft-°F). It can be measured using specialized equipment, such as a thermal conductivity meter, or calculated using known values for the material's specific heat and thermal diffusivity.

3. What factors affect the thermal conductivity of a metal rod?

The thermal conductivity of a metal rod can be affected by several factors, including the material's composition, temperature, and crystal structure. Generally, materials with higher thermal conductivity have a higher density and a more regular arrangement of atoms, which allows for easier heat transfer.

4. How does the thermal conductivity of a metal rod affect its practical applications?

The thermal conductivity of a metal rod is an important consideration in many practical applications, such as in heating and cooling systems, cooking utensils, and electronic devices. Materials with higher thermal conductivity are more efficient at transferring heat, making them ideal for applications where heat needs to be transferred quickly and efficiently.

5. Can the thermal conductivity of a metal rod change over time?

In most cases, the thermal conductivity of a metal rod will remain relatively constant over time. However, some factors, such as temperature and corrosion, can affect the thermal conductivity of a metal over time. For example, as a metal rod is heated, its thermal conductivity may decrease due to thermal expansion and the change in crystal structure. Similarly, corrosion can create barriers to heat transfer and decrease the thermal conductivity of a metal over time.

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