# This is in spite of the fact that both w and as we

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. This is in spite of the fact that both W and, as we will see later, Q are path-dependent quantities. Therefore, we can deduce that this defines energy : a thermodynamic property which is a theoretical construct suggested by the first law of thermodynamics as something to account for the difference between heat transfer and work in any process between the same start and end states. Energy is a new extensive property of the system denoted by E . While we like to think we have intuition for what constitutes energy, it really is an elusive quantity. Viewed at another way, the Newtonian mechanical energy is easily visualized in terms of kinetic and potential energy, but it is not always conserved! Our new energy includes thermal energy, which we think we can easily feel, so we still have a good intuition for it. So we have generalized energy so that it is always conserved, at the expense of losing the ability to easily visualize it. Recall that properties depend only on the state and not the path taken to arrive at the state. Let us then take the following definition for the differential of E : dE = δQ δW. (5.8) If we integrate from 1 to 2, we get integraldisplay 2 1 dE = integraldisplay 2 1 δQ integraldisplay 2 1 δW. (5.9) yielding E 2 E 1 = 1 Q 2 1 W 2 . (5.10) Equation (5.10) is the alternate representation of the First law of thermodynamics : For a system undergoing a process, the change in energy is equal to the heat added to the system minus the work done by the system. Now we consider E to represent the total energy of the system. It has units of J . It includes energy which is potential, kinetic, thermal, chemical, electrical, magnetic, CC BY-NC-ND. 2011, J. M. Powers.

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108 CHAPTER 5. THE FIRST LAW OF THERMODYNAMICS etc. We will find it useful to lump all of these other types of energy into a single term U , which we call internal energy : that portion of total energy E which is not kinetic or potential energy. It includes thermal, chemical, electric, magnetic, and other forms of energy. We take U to have units of J . We call the kinetic energy KE and the potential energy PE . So we take E bracehtipupleftbracehtipdownrightbracehtipdownleftbracehtipupright total energy = U bracehtipupleftbracehtipdownrightbracehtipdownleftbracehtipupright internal energy + KE bracehtipupleftbracehtipdownrightbracehtipdownleftbracehtipupright kinetic energy + PE bracehtipupleftbracehtipdownrightbracehtipdownleftbracehtipupright potential energy . (5.11) In this course we shall mainly be concerned with changes of U which are associated with changes of the thermal energy of the system. A useful way to think of thermal energy is Thermal energy : kinetic energy associated with random motions of molecules at the microscale .
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