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Internal energy U

We can think about the internal energy of a system in two different but consistent ways. The first is the atomic and molecular view, which examines the system on the atomic and molecular scale. The internal energy     U size 12{U} {} of a system is the sum of the kinetic and potential energies of its atoms and molecules. Recall that kinetic plus potential energy is called mechanical energy. Thus internal energy is the sum of atomic and molecular mechanical energy. Because it is impossible to keep track of all individual atoms and molecules, we must deal with averages and distributions. A second way to view the internal energy of a system is in terms of its macroscopic characteristics, which are very similar to atomic and molecular average values.

Macroscopically, we define the change in internal energy Δ U size 12{ΔU} {} to be that given by the first law of thermodynamics:

Δ U = Q W . size 12{ΔU=Q - W} {}

Many detailed experiments have verified that Δ U = Q W size 12{ΔU=Q - W} {} , where Δ U size 12{ΔU} {} is the change in total kinetic and potential energy of all atoms and molecules in a system. It has also been determined experimentally that the internal energy U size 12{U} {} of a system depends only on the state of the system and not how it reached that state . More specifically, U size 12{U} {} is found to be a function of a few macroscopic quantities (pressure, volume, and temperature, for example), independent of past history such as whether there has been heat transfer or work done. This independence means that if we know the state of a system, we can calculate changes in its internal energy U size 12{U} {} from a few macroscopic variables.

Making connections: macroscopic and microscopic

In thermodynamics, we often use the macroscopic picture when making calculations of how a system behaves, while the atomic and molecular picture gives underlying explanations in terms of averages and distributions. We shall see this again in later sections of this chapter. For example, in the topic of entropy, calculations will be made using the atomic and molecular view.

To get a better idea of how to think about the internal energy of a system, let us examine a system going from State 1 to State 2. The system has internal energy U 1 size 12{U rSub { size 8{1} } } {} in State 1, and it has internal energy U 2 size 12{U rSub { size 8{2} } } {} in State 2, no matter how it got to either state. So the change in internal energy Δ U = U 2 U 1 size 12{ΔU=U rSub { size 8{2} } - U rSub { size 8{1} } } {} is independent of what caused the change. In other words, Δ U size 12{ΔU} {} is independent of path . By path, we mean the method of getting from the starting point to the ending point. Why is this independence important? Note that Δ U = Q W size 12{ΔU=Q - W} {} . Both Q size 12{Q} {} and W size 12{W} {} depend on path , but Δ U size 12{ΔU} {} does not. This path independence means that internal energy U size 12{U} {} is easier to consider than either heat transfer or work done.

Calculating change in internal energy: the same change in U size 12{U} {} Is produced by two different processes

(a) Suppose there is heat transfer of 40.00 J to a system, while the system does 10.00 J of work. Later, there is heat transfer of 25.00 J out of the system while 4.00 J of work is done on the system. What is the net change in internal energy of the system?

(b) What is the change in internal energy of a system when a total of 150.00 J of heat transfer occurs out of (from) the system and 159.00 J of work is done on the system? (See [link] ).

Questions & Answers

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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