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

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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

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� � � � �� �

� �� � �� � �� ��� �

� The work done by the engine in a complete cycle is the area enclosed by the curve representingthe process on a PV diagram

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Thermodynamic Efficiency of a Heat Engine� The thermodynamic efficiency � of the engine is the ratio of the work done to the heat absorbed

per cycle

� � �� ��� � � �� � �� ��� �

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� Example: An automobile engine, whose thermal efficiency is 22.0 %, operates at 95 cycles persecond and does work at the rate of 120 horse power. (a) How much work per cycle does theengine do? (b) How much heat does the engine absorb per cycle? (c) How much heat is rejectedby the engine per cycle?

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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 donevery slowly by dropping grains of sand onto a frictionless piston

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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

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The Carnot Cycle� Process A � B is an isothermal expansion at temperature � �

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� Process B � C is an adiabatic expansion (� " $ � )

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� Process C � D is an isothermal compression at �� ( ��� � &

�� � � $' % �

� Process D � A is an adiabatic compression (� ' ! � )

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� The net work done by the engine � �� � is the area bounded by the curves on a PV diagram or

� �� � �� � �� ��� �

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Carnot Efficiency� In the Carnot cycle heat is absorbed and ejected only during isothermal processes and therefore

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� The thermal efficiency of a Carnot engine is then

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Example

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

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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

� �� � �� ��� �

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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 tothe work required to transfer that energy

�* + ,.- �� � /102 / & �� � ��

� A Carnot engine operating in reverse constitutes an ideal heat pump with the highest possibleCOP for the temperatures between which it operates

�* + $ () �3 � , - �� � /102 / & � �� �� ��

� The COP for a refrigerator is defined as the ratio of the heat extracted from the cold reservoir tothe work required to extract that energy

�* + ,� � 4 � � 5 � �� �6 � & ��� ��

� A Carnot engine operating in reverse constitutes an ideal refrigerator with the highest possibleCOP for the temperatures between which it operates

�* + $ () �3 � ,� � 4 � � 5 � �� �6 � & ��� �� ��

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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 performanceof an equal amount of work."

� Clausius statement: "Energy does not flow spontaneously from a cold object to a hot object."

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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

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