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We know that the property of a fluid at a point is the mean of this quantity over a small volume centered around this point. For internal energy is it also the mean or it is the sum of the internal energies inside the small volume?

Tonylb1
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1 Answers1

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Internal energy is an extensive property. That is, it depends on the mass of your sample. If you have a container of fluid and you take a small sample, the internal energy in the sample is smaller than the internal energy stored in the entire container.

Volume is another example of an extensive property.

These differ from intensive properties, which do NOT depend on the mass of your sample. Temperature and density are examples of intensive properties. Although density is given by mass/volume, if you sample more mass of your fluid, you will automatically be sampling a larger volume, such that the [mass sampled]/[volume sampled] equals a constant density regardless of the mass of your sample. Temperature is a measure of the average kinetic energy of molecules, and so does not depend on the number of molecules sampled.

Internal energy is a total, not an average. In a fluid, the internal energy is the sum of the internal energy (in turn, the sum of the kinetic and potential energy) of each molecule.

See http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/temper.html#c1 for a detailed discussion of kinetic energy and temperature. At the bottom of the page, it shows the relationship between these quantities and internal energy.

Burrito
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  • Great. For heat conduction rate, it is the gradient of the temperature and the temperature is an average property so the heat conduction rate is an average? – Tonylb1 Oct 24 '15 at 06:14