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Lecture 1: Energy Reading: Zumdahl 9.1 Outline –Energy: Kinetic and Potential –System vs. Surroundings –Heat, Work, and Energy

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Energy: Kinetic vs. Potential Potential Energy (PE) –Energy due to position or composition. –Equals (mgh) in this example. Kinetic Energy (KE) –Energy due to motion. –Equals ( 1/2 )mv 2 in this example.

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Energy = KE + PE Energy is the sum of kinetic energy and potential energy. Energy is readily interconverted between these two forms. If the system of interest is isolated (no exchange with surroundings), then total energy of the system is constant.

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Example: Mass on a Spring Initial PE = 1/2 kx 2 At x = 0: –PE = 0 –KE = 1/2mv 2 =1/2kx 2 Units of Energy Joule = kg.m 2 /s 2 Example: –Init. PE = 10 J –M = 10 kg –Vmax = [2(PE)/M] 1/2 = 1.4m/s 0 E(x) = PE(x) + KE(x)

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First Law of Thermodynamics First Law: Energy of the Universe is Constant ∆ E = q + w (remember this!) q = heat. Energy transferred between two bodies of differing temperature. (Note: q ≠ Temp!) w = work. Force acting over a distance (F x d)

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Applying the First Law Need to differentiate between the system and surroundings. System: That part of the universe you are interested in (i.e., you define it). Surroundings: The rest of the universe.

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Conservation of Energy Total energy is conserved. Energy gained by the system must be lost by the surroundings. Energy exchange can be in the form of q, w, or both.

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Heat Exchange: Exothermic Exothermic Reaction. a process in which heat is transferred from the system to the surroundings. q < 0 (heat is lost from the system)

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Another Example of Exothermic

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Heat Exchange: Endothermic Endothermic Reaction: a process in which heat is transferred from the surroundings to the system. q > 0 (heat is gained by the system)

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Another Example of Endothermic

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Energy and Sign Convention If system loses energy: E final < E initial E final -E initial = E < 0. If system gains energy: E final > E initial E final -E initial = E > 0.

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Heat and Work Sign Convention Heat (q) If system gives heat q < 0 (q is negative) If system gets heat q > 0 (q is positive) Work (w) If system does work w < 0 (w is negative) If work done on system w > 0 (w is positive)

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Example: piston doing PV work Figure 9.4, expansion against a constant external pressure No heat exchange: q = 0 (adiabatic) System does work: w < 0

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How much work does the system do? P ext = force/area |w| = force x distance = P ext x A x h = P ext V w = - P ext V (note sign)

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Example 9.1 A balloon is inflated from 4 x 10 6 l to 4.5 x 10 6 l by the addition of 1.3 x 10 8 J of heat. If the balloon expands against an external pressure of 1 atm, what is E for this process? Ans: First, define the system: the balloon.

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E = q + w = (1.3 x 10 8 J) + (-P V) = (1.3 x 10 8 J) + (-1 atm (V final V init )) = (1.3 x 10 8 J) + (-0.5 x 10 6 l.atm) Conversion: 101.3 J per l.atm (-0.5 x 10 6 l.atm) x (101.3 J/l.atm) = -5.1 x 10 7 J E = (1.3 x 10 8 J) + (-5.1 x 10 7 J) = +8 x 10 7 J (Ans.) (In plain English) the system gained more energy through heat than it lost doing work. Therefore, the overall energy of the system has increased.

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Constant Volume Processes For a constant volume process, the change in internal energy of the system is equal to the heat (q) transferred. No PV work is possible, since there is no change in volume. What if the volume of the system is held constant? E = q + w = q V 0 “constant V”

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