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handout_L04_Entropy2 - Lecture 4 Thermo and Entropy Reading...

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Lecture 4: Thermo and Entropy Reading: Zumdahl 10.2, 10.3 • Outline – Isothermal processes – Isothermal gas expansion and work – Reversible Processes Isothermal Processes • Recall: Isothermal means T = 0. • Since E = nC v T, then E = 0 for an isothermal process. • Since E = q + w: q = -w (isothermal process) Example: Isothermal Expansion Consider a mass connected to a ideal gas contained in a “piston”. Piston is submerged in a constant T bath such that T = 0. Isothermal Expansion (cont.) Initially, V = V 1 P = P 1 Pressure of gas is equal to that created by mass: P 1 = force/area = M 1 g/A where A = piston area g = gravitational acceleration (9.8 m/s 2 ) Isothermal Expansion (cont.) One-Step Expansion. We change the weight to M 1 /4, then P ext = (M 1 /4)g/A = P 1 /4 The mass will be lifted until the internal pressure equals the external pressure. In this case V final = 4V 1 w = -P ext V = -P 1 /4 (4V 1 - V 1 ) = -3/4 P 1 V 1 Two Step Expansion In this expansion we go in two steps: Step 1: M 1 to M 1 /2 Step 2: M 1 /2 to M 1 /4 In first step: P ext = P 1 /2, V final = 2V 1 • w 1 = -P ext V = -P 1 /2 (2V 1 - V 1 ) = -1/2 P 1 V 1
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Two Step Expansion (cont.) In Step 2 (M 1 /2 to M 1 /4 ): P ext = P 1 /4, V final = 4V 1 • w 2 = -P ext V =- P 1 /4 (4V 1 - 2V 1 ) = -1/2 P 1 V 1 • w total = w 1 + w 2 = -P 1 V 1 /2 - P 1 V 1 /2 = -P 1 V 1 • w total,2 step > w
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