Heat Engines and the Second Law of Thermodynamics Heat Engines - - PowerPoint PPT Presentation

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

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

Thermodynamic Efficiency of a Heat Engine

• The thermodynamic efficiency

• f the engine is the ratio of the work done to the heat absorbed

per cycle

• 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?

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 thermody- namic 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

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

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

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

Example

Consider a Carnot engine that operates between the temperatures

= 850 K and

= 300 K. The 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?

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

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

• A Carnot engine operating in reverse constitutes an ideal heat pump with the highest possible

COP for the temperatures between which it operates

• 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

• A Carnot engine operating in reverse constitutes an ideal refrigerator with the highest possible

COP for the temperatures between which it operates

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

• f an equal amount of work."
• Clausius statement: "Energy does not flow spontaneously from a cold object to a hot object."

Homework Set 8 - Due Wed. Jan. 28

• Read Sections 18.1 - 18.5
• Answer Questions 18.2, 18.3 & 18.6
• Do Problems 18.2, 18.7, 18.12 & 18.16