What is the rate of heat conduction through a 30 m thickness of rhyolite lava?

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In summary, the problem involves calculating the rate of heat conduction through a 30 m thickness of rhyolite, with a surface temperature of 400 degrees Celsius and an interior temperature of 3100 degrees Celsius. The thermal conductivity of rhyolite is 0.84 Wm^-1 degrees Celsius^-1. Using the equation P = kA (dT/dx), the correct answer is 75.6 W/m^2, obtained by dividing the temperature gradient (2700 degrees Celsius) by the thickness (30 m) and multiplying by the thermal conductivity and the area.
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roam
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Homework Statement



A lava beds cool very slowly, remaining warm for years. Calculate the rate of heat conduction per square metre through a 30 m thickness of rhyolite, if the surface is 400 degrees celcius and its interior side is at 3100 degrees celcius. The thermal conductivity of rhyolite =0.84 Wm^-1 degrees celcius^-1.

Answer must be 75.6 W/m^2


Homework Equations



[tex]P=kA \left| \frac{dT}{dx}\right|[/tex]

(The rate is P, k is thermal conductivity, dT/dx is temprature gradient)

The Attempt at a Solution



dT/dx = 3100-400 = 2700

[tex]0.84 \times 30 \times(2700) = 68040[/tex]

Can anyone show me the problem? ...because the right answer is 75.6!
 
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  • #2
Why are you multiplying by 30 instead of dividing? dT/dx is 2700/30.
 
  • #3
ideasrule said:
Why are you multiplying by 30 instead of dividing? dT/dx is 2700/30.

Yes, but I need a number for area A!
 
  • #4
Oh, never mind I get it. THANKS!
 

1. How does lava conductive cooling work?

Lava conductive cooling is a process in which heat is transferred from the hot lava to cooler surrounding materials through direct contact. The lava's high temperature causes the molecules in the surrounding materials to vibrate and gain energy, resulting in a temperature increase in the surrounding area.

2. What factors affect the rate of lava conductive cooling?

The rate of lava conductive cooling is influenced by several factors, including the lava's initial temperature, the temperature and composition of the surrounding materials, the thickness of the surrounding materials, and the surface area of contact between the lava and the surrounding materials.

3. Can lava conductive cooling be used to generate energy?

Yes, lava conductive cooling can be used to generate energy through a process called geothermal energy. This involves drilling into the Earth's crust to access hot rocks or lava, and using the heat from the lava to produce steam that can power turbines and generate electricity.

4. Is lava conductive cooling a fast or slow process?

The speed of lava conductive cooling depends on several factors, including the initial temperature of the lava and the composition and thickness of the surrounding materials. In general, it is considered a relatively slow process compared to other forms of heat transfer such as convection or radiation.

5. How does lava conductive cooling affect the formation of volcanic rocks?

Lava conductive cooling plays a significant role in the formation of volcanic rocks. As the lava cools and solidifies, it forms different types of rocks depending on the rate of cooling and the composition of the lava. For example, slow cooling can lead to the formation of large crystals, while rapid cooling can result in smaller crystals or even glassy rocks.

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