Lecture15-08.2-Heat_engines-Enthalpy-Gibbs_energy

Lecture15-08.2-Heat_engines-Enthalpy-Gibbs_energy - LECTURE...

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1 Announcements Monday, Oct. 25, in class. Covers Lectures 1-15 Chapters 1-8 Midterm LECTURE 15 Bring: calculator equation sheet (make your own) Last Time LECTURE 15 Carnot Efficiency: 1 out h l l C h h h W Q τ τ τ η τ τ - = = = - Maximum power: 1 L H τ η τ = - Carnot Inequality: C η η Carnot Cycle & diagrams Carnot Coefficient: Heat Engines Refrigerators and Heat Pumps l l C h l Q W τ γ τ τ = = -
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2 Today Chapter 8 (part 2) Heat and Work: Heat Engines LECTURE 15 Heat engines: what possible Work in Carnot cycle: ideal gas example Path dependence of heat and work Irreversible and reversible work Isothermal, isobaric heat and work Enthalpy and free Gibbs energy Electrolysis and fuel cell Chemical work Magnetic work and superconductors Carnot Cycle: Engine 1-2. Isothermal expansion 1 out in W Q τ σ = = Δ ( ) max min h τ σ σ = - 2 2-3. Isentropic expansion 3 3 2 out W U N τ = -Δ = - Δ ( ) 3 2 l h N τ τ = - - 3-4. Isothermal compression out in W Q τ σ = = Δ 4 ( ) min max l τ σ σ = - 4-1. Isentropic compression 3 2 out W U N τ = -Δ = - Δ ( ) 3 2 h l N τ τ = - - HEAT HEAT
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3 Carnot Cycle: Refrigerator 1-2. Isothermal expansion 4 in out Q W τ σ = Δ = ( ) max min h τ σ σ = - 3 2-3. Isentropic compression 2 3 2 out W U N τ = -Δ = - Δ ( ) 3 2 h l N τ τ = - - 3-4. Isothermal compression out in W Q τ σ = = Δ 1 ( ) min max l τ σ σ = - 4-1. Isentropic expansion 3 2 out W U N τ = -Δ = - Δ ( ) 3 2 l h N τ τ = - - HEAT HEAT Carnot Cycle Heat = Area Isentropic Isentropic Isothermal Isothermal Work = Area
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4 YES! What’s possible 1. Can you completely convert work into heat? 2. Can you completely convert heat into work? Work Heat Device Heat Work Device Hint: think about what happens to the entropy NO! What’s possible Can we have two reversible cyclic devices that have different efficiencies?
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5 Example: Carnot Cycle for a Monatomic Ideal Gas Find the work during the cycle, in terms of 1 4 3 2 1-2. Isothermal Expansion from 1 to 2: dU d pdV dN τ σ μ = - + 2 1 12 V V W pdV = = V 1 V 2 V 4 V 3 pV N τ = 2 1 1 V h V N dVd V τ σ = p N V τ = Example: Carnot Cycle for a Monatomic Ideal Gas Find the work during the cycle, in terms of 1 4 3 2 1-2. Isothermal Expansion from 1 to 2: Alternatively: Internal energy cannot change, so W = Q dU d pdV dN τ σ μ = - + ( ) 12 2 1 log h W N V V τ = V 1 V 2 V 4 V 3 ( ) 12 max min h Q τ σ σ = - ( ) 12 2 1 12 log h Q N V V W τ = =
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6 Example: Carnot Cycle for a Monatomic Ideal Gas Find the work during the cycle, in terms of 1 4 3 2 2-3. Isentropic Expansion: dU d pdV dN τ σ μ = - + 2 1 23 V V W pdV = V 1 V 2 V 4
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