Heat Engines and the Second Law of Thermodynamics

Transcription

1 Heat Engines and the Second Law of Thermodynamics Heat Engines Reversible and Irreversible Processes The Carnot Engine Refrigerators and Heat Pumps The Second Law of Thermodynamics Homework

2 Heat Engines A heat engine is a device that, operating in a cycle, extracts energy as heat from a hot reservoir, does a certain amount of work, and ejects energy as heat to a cold reservoir For a complete cycle and from the first law The work done by the engine in a complete cycle is the area enclosed by the curve representing the process on a PV diagram

3 Thermodynamic Efficiency of a Heat Engine The thermodynamic efficiency per cycle of the engine is the ratio of the work done to the heat absorbed Example: An automobile engine, whose thermal efficiency is 22.0 %, operates at 95 cycles per second and does work at the rate of 120 horse power. (a) How much work per cycle does the engine do? (b) How much heat does the engine absorb per cycle? (c) How much heat is rejected by the engine per cycle?

4 Reversible and Irreversible Processes A reversible process is one that proceeds so slowly that every intermediate state is in equilibrium. Therefore, every intermediate state can be exactly described by a set of macroscopic thermodynamic variables. Since every intermediate state is know, the process may be reversed. An irreversible process is one that does not satisfy these conditions. An example of a reversible process is shown below - the isothermal compression of a gas is done very slowly by dropping grains of sand onto a frictionless piston

5 The Carnot Engine A heat engine operating in a Carnot cycle between two heat reservoirs is the most efficient engine possible Consider a system composed of an ideal gas confined in a cylinder fitted with a movable piston The Carnot cycle consists of two isothermal and two adiabatic paths

6 & '! # $' % " $ % "! # The Carnot Cycle Process A B is an isothermal expansion at temperature Process B C is an adiabatic expansion ( " $ ) Process C D is an isothermal compression at Process D A is an adiabatic compression ( '! ) The net work done by the engine is the area bounded by the curves on a PV diagram or (

7 )( Carnot Efficiency In the Carnot cycle heat is absorbed and ejected only during isothermal processes and therefore The thermal efficiency of a Carnot engine is then

8 Example Consider a Carnot engine that operates between the temperatures engine performs 1200 J of work each cycle, which takes 0.25 s. (a) What is the efficiency of the engine? (b) What is the average power of the engine? (c) How much energy is extracted as heat from the high temperature reservoir each cycle? (d) How much energy is delivered as heat to the low temperature reservoir each cycle? = 850 K and = 300 K. The

9 Refrigerators and Heat Pumps A refrigerator or heat pump is a device that, operating in a cycle, has work done on it as it extracts energy as heat from a cold reservoir and ejects energy as heat to a hot reservoir The net work performed on the refrigerant to extract heat is

10 * + Coefficient of Performance The effectiveness of a refrigerator or heat pump is described by the coefficient of performance or COP The COP for a heat pump is defined as the ratio of the heat transferred into the hot reservoir to the work required to transfer that energy,.- /102 $ 3 )( * + / & A Carnot engine operating in reverse constitutes an ideal heat pump with the highest possible COP for the temperatures between which it operates, - /102 * + / & The COP for a refrigerator is defined as the ratio of the heat extracted from the cold reservoir to the work required to extract that energy, 4 $ 3 )( * + & 5 6 A Carnot engine operating in reverse constitutes an ideal refrigerator with the highest possible COP for the temperatures between which it operates, 4 & 5 6

11 The Second Law of Thermodynamics Kelvin-Planck statement: "It is impossible to construct a heat engine that, operating in a cycle, produces no other effect other than the absorption of energy from a reservoir and the performance of an equal amount of work." Clausius statement: "Energy does not flow spontaneously from a cold object to a hot object."

12 Read Sections Answer Questions 18.2, 18.3 & 18.6 Do Problems 18.2, 18.7, & Homework Set 8 - Due Wed. Jan. 28