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notes_Lecture_03_100610_revised

# notes_Lecture_03_100610_revised - Lecture 3 Thermodynamics...

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Lecture 3: Thermodynamics of Ideal Gases & Calorimetry • Announcements – Calculators – Homework • Reading: Zumdahl 9.3, 9.4 • Outline Define the manner in which substances “store” heat energy: heat capacity ( C V , C P ) Mathematical form for Δ E and Δ H using C V and C P Thermodynamics of Ideal Gases (9.3) State Functions Example of Thermo. Pathways Calorimetry (9.4)

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Heat Capacity for Monatomic Ideal Gases Constant V Heat Capacity: C V = “heat into translation” = 3/2 R Constant P Heat Capacity: C P = “heat into translation” + “work” = C V + R = (5/2) R
Variation in C p and C v Monatomic: C V = (3/2)R and C P = (5/2)R Polyatomic*: C V > (3/2)R and C P > (5/2)R For Gases: C P = C V + R (J mol -1 K -1 ) (J mol -1 K -1 ) *Polyatomic molecules experience rotational and vibrational motion in addition to translational motion (additional degrees of freedom).

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Energy and C V Recall from Chapter 5: E ave = 3/2 nRT (average trans. energy) Δ E = 3/2 nR Δ T Δ E = n C V Δ T (since 3/2 R = C v ) Why is it C V ? We envision heating our system at constant volume. As such, all heat goes towards increasing E (no work is performed). The heat we add goes into increasing the translational KE only . In other words, the heat transferred at constant volume is exactly equal to the change in internal energy, Δ E: q V = Δ E = nC V Δ T (at const V)
Enthalpy and C P What if we heated our gas at constant pressure? Then, we have a volume change, which means work occurs. q p = n C P Δ T = n (C V + R) Δ T = nC V Δ T + nR Δ T = Δ E + P Δ V = Δ H barb2right q P = Δ H = nC P Δ T Here, the heat we add goes into increasing the translational KE and performing PV-work. The heat transferred at constant pressure is exactly equal to the change in enthalpy, Δ H.

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Keeping Track Ideal Monatomic Gas • C V = (3/2)R • C P = C V + R = (5/2)R Polyatomic Gas • C V > (3/2)R • C P > (5/2)R All Ideal Gases Δ E = nC V Δ T Δ H = nC P Δ T
Suppose that you have two identical 500-mL bottles of water sitting on your desk at equilibrium with the surroundings. Bottle 1 has been kept at 25°C since bottling. Bottle 2 came from the same spring, but has been frozen, thawed, transported by air in an unpressurized compartment, and allowed to fluctuate wildly in temperature before being at equilibrium on your desk. Which bottle experienced the most heat flow? Which bottle has the higher internal energy?

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State Functions vs. Process Functions State Function : a thermodynamic quantity that depends only on the initial and final states of the system, not on its history… the value of a state function does not depend in how we put the system into the current state.
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