Thermodynamics and Statistical Mechanics Heat Engines and Refrigerators

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Thermodynamics and Statistical Mechanics Heat Engines and Refrigerators Thermo & Stat Mech Spring 2006

Thermodynamics and Statistical Mechanics Heat Engines and Refrigerators Thermo & Stat Mech Spring 2006 Class 5 1

Carnot Cycle A Carnot cycle is an idealized reversible cycle that operates between two

Carnot Cycle A Carnot cycle is an idealized reversible cycle that operates between two heat reservoirs at temperatures T 1 and T 2, where T 2 > T 1. It can operate as a heat engine, or a refrigerator. Thermo & Stat Mech - Spring 2006 Class 5 2

Carnot Cycle Thermo & Stat Mech - Spring 2006 Class 5 3

Carnot Cycle Thermo & Stat Mech - Spring 2006 Class 5 3

Carnot Cycle (Heat Engine) Thermo & Stat Mech - Spring 2006 Class 5 4

Carnot Cycle (Heat Engine) Thermo & Stat Mech - Spring 2006 Class 5 4

Carnot Cycle Thermo & Stat Mech - Spring 2006 Class 5 5

Carnot Cycle Thermo & Stat Mech - Spring 2006 Class 5 5

Carnot Cycle For the entire cycle, Q = W + DU, and DU =

Carnot Cycle For the entire cycle, Q = W + DU, and DU = 0. The total heat equals the total work, Q = W. |W| = |Q 2| – |Q 1| Conservation of energy. |Q 2| = |Q 1| + |W| Thermo & Stat Mech - Spring 2006 Class 5 6

Carnot Cycle For an isothermal process: For an adiabatic process: Thermo & Stat Mech

Carnot Cycle For an isothermal process: For an adiabatic process: Thermo & Stat Mech - Spring 2006 Class 5 7

Path a®b Thermo & Stat Mech - Spring 2006 Class 5 8

Path a®b Thermo & Stat Mech - Spring 2006 Class 5 8

Paths b®c, c®d, and d®a Thermo & Stat Mech - Spring 2006 Class 5

Paths b®c, c®d, and d®a Thermo & Stat Mech - Spring 2006 Class 5 9

Carnot Cycle Divide a®b by c®d and then b®c by d®a, and Thermo &

Carnot Cycle Divide a®b by c®d and then b®c by d®a, and Thermo & Stat Mech - Spring 2006 Class 5 10

Thermal Efficiency (h) If T 1 = 0, h = 1 (100%) Thermo &

Thermal Efficiency (h) If T 1 = 0, h = 1 (100%) Thermo & Stat Mech - Spring 2006 Class 5 11

Refrigerator (Heat Pump) Run the cycle in reverse. Do work |W| on the system,

Refrigerator (Heat Pump) Run the cycle in reverse. Do work |W| on the system, remove |Q 1| from the low temperature reservoir, and put |Q 2| into the high temperature reservoir. As in a heat engine, |Q 2| = |Q 1| + |W|. Thermo & Stat Mech - Spring 2006 Class 5 12

Coefficient of Performance (for Refrigerator) Thermo & Stat Mech - Spring 2006 Class 5

Coefficient of Performance (for Refrigerator) Thermo & Stat Mech - Spring 2006 Class 5 13

Coefficient of Performance (for Heat Pump) Thermo & Stat Mech - Spring 2006 Class

Coefficient of Performance (for Heat Pump) Thermo & Stat Mech - Spring 2006 Class 5 14

Otto Cycle (Gasoline Engine) Thermo & Stat Mech - Spring 2006 Class 5 15

Otto Cycle (Gasoline Engine) Thermo & Stat Mech - Spring 2006 Class 5 15

Otto Cycle W = |Q 2| – |Q 1| |Q 2| = CV(Tc –

Otto Cycle W = |Q 2| – |Q 1| |Q 2| = CV(Tc – Tb) |Q 1| = CV(Td – Ta) Thermo & Stat Mech - Spring 2006 Class 5 16

Otto Cycle Thermo & Stat Mech - Spring 2006 Class 5 17

Otto Cycle Thermo & Stat Mech - Spring 2006 Class 5 17

Otto Cycle and Subtract, and get, Then, Thermo & Stat Mech - Spring 2006

Otto Cycle and Subtract, and get, Then, Thermo & Stat Mech - Spring 2006 Class 5 18

Otto Cycle is called the compression ratio. Thermo & Stat Mech - Spring 2006

Otto Cycle is called the compression ratio. Thermo & Stat Mech - Spring 2006 Class 5 19

Diesel Cycle Thermo & Stat Mech - Spring 2006 Class 5 20

Diesel Cycle Thermo & Stat Mech - Spring 2006 Class 5 20

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