Lecture 36

General Physics (PHY 2130)

http://www.physics.wayne.edu/~apetrov/PHY2130/

•  The laws of thermodynamics

  Heat Engines   Carnot cycle

Lightning Review

Last lecture: 1.  Thermodynamics

  Heat and work. First Law of Thermodynamics: ΔU = Q + W   Isothermal, adiabatic, isobaric and isochoric processes.

Review Problem: An ideal gas is in contact with a heat reservoir so that it remains at constant temperature of 300.0 K. The gas is compressed from a volume of 24.0 L to a volume of 14.0 L. During the process, the mechanical device pushing the piston to compress the gas is found to expend 5.00 kJ of energy. How much heat flows between the heat reservoir and the gas, and in what direction does the heat flow occur?

This is an isothermal process, so ΔU = Q + W = 0 (for an ideal gas) and W = -Q = -5.00 kJ. Heat flows from the gas to the reservoir.

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Reversible and Irreversible Processes

A process is reversible if it does not violate any law of physics when it is run backwards in time.

Example 1: a collision between two billiard balls is reversible. Momentum is conserved if time is run forward; momentum is still conserved if time runs backwards.

Example 2: an ice cube placed on a countertop in a warm room will melt. The reverse process cannot occur: an ice cube will not form out of the puddle of water on the countertop in a warm room.

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Any process that involves dissipation of energy is not reversible.

Any process that involves heat transfer from a hotter object to a colder object is not reversible.

The second law of thermodynamics (Clausius):

Heat never flows spontaneously from a colder body to a hotter body.

Heat Engines • A heat engine is a device that converts internal energy to

other useful forms, such as electrical or mechanical energy

• A heat engine is a device designed to convert disordered energy into ordered energy. The net work done by an engine during one cycle is equal to the net heat flow into the engine during the cycle (ΔU = 0).

• A heat engine carries some working substance through a cyclical process

netnet QW =

Let’s watch the movie!

Heat Engine

• Energy is transferred from a source at a high temperature (Qh)

• Work is done by the engine (Weng)

• Energy is expelled to a source at a lower temperature (Qc)

Heat Engine

• Since it is a cyclical process, ΔU = 0 •  Its initial and final internal

energies are the same •  Therefore, Qnet = Weng •  The work done by the

engine equals the net energy absorbed by the engine

•  The work is equal to the area enclosed by the curve of the PV diagram

Thermal Efficiency of a Heat Engine •  Thermal efficiency (or simply effciency) is defined as the

ratio of the work done by the engine to the energy absorbed at the higher temperature

or

•  e = 1 (100% efficiency) only if Qc = 0 •  No energy expelled to cold reservoir

h

c

h

ch

h

eng

QQ

1QQQ

QW

−=−

== e

.inputheat

engine by the donenet work

in

net

QW

e ==

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Example: (a) How much heat does an engine with efficiency of 33.3 % absorb in order to deliver 1.00 kJ of work? (b) How much heat is exhausted by the engine?

kJ 00.30.333

kJ 00.1netH ===

eW

Q

(b) How much heat is exhausted by the engine?

( ) kJ 00.21

1

HC

H

C

=−=

−=

QeQ

QQ

e

Idea: use the formula for the efficiency of the heat engine:

Second Law of Thermodynamics

•  It is impossible to construct a heat engine that, operating in a cycle, produces no other effect than the absorption of energy from a reservoir and the performance of an equal amount of work

•  Means that Qc cannot equal 0 •  Some Qc must be expelled to the environment

•  Means that e cannot equal 100%

Heat Pumps and Refrigerators

• Heat engines can run in reverse • Send in energy • Energy is extracted from the cold reservoir • Energy is transferred to the hot reservoir

• This process means the heat engine is running as a heat pump • A refrigerator is a common type of heat pump • An air conditioner is another example of a heat

pump

Summary of the First and Second Laws •  First Law

•  We cannot get a greater amount of energy out of a cyclic process than we put in

• Second Law •  We cannot break even

Carnot Engine • A theoretical engine developed by Sadi Carnot • A heat engine operating in an ideal, reversible cycle (now called a Carnot Cycle) between two reservoirs is the most efficient engine possible

• Carnot’s Theorem: No real engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs

Carnot Cycle

Let’s watch the movie!

Carnot Cycle, A to B

• A to B is an isothermal expansion

•  The gas is placed in contact with the high temperature reservoir

•  The gas absorbs heat Qh •  The gas does work WAB

in raising the piston

Carnot Cycle, B to C

• B to C is an adiabatic expansion

•  The base of the cylinder is replaced by a thermally nonconducting wall

• No heat enters or leaves the system

•  The temperature falls from Th to Tc

•  The gas does work WBC

Carnot Cycle, C to D

• The gas is placed in contact with the cold temperature reservoir

• C to D is an isothermal compression

• The gas expels energy QC • Work WCD is done on the gas

Carnot Cycle, D to A

• D to A is an adiabatic compression

•  The gas is again placed against a thermally nonconducting wall •  So no heat is exchanged with

the surroundings

•  The temperature of the gas increases from TC to Th

•  The work done on the gas is WCD

Carnot Cycle, PV Diagram

• The work done by the engine is shown by the area enclosed by the curve

• The net work is equal to Qh - Qc

Efficiency of a Carnot Engine

• Carnot showed that the efficiency of the engine depends on the temperatures of the reservoirs

•  Temperatures must be in Kelvins • All Carnot engines operating between the same two

temperatures will have the same efficiency

h

Cc T

Te −=1

Notes About Carnot Efficiency

• Efficiency is 0 if Th = Tc • Efficiency is 100% only if Tc = 0 K

•  Such reservoirs are not available

•  The efficiency increases at Tc is lowered and as Th is raised

•  In most practical cases, Tc is near room temperature, 300 K •  So generally Th is raised to increase efficiency

Real Engines Compared to Carnot Engines

• All real engines are less efficient than the Carnot engine •  Real engines are irreversible because of friction •  Real engines are irreversible because they complete cycles in

short amounts of time

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Example: An engine operates between temperatures 650 K and 350 K at 65.0% of its maximum efficiency. (a) What is the efficiency of this engine? (b) If 6.3×103 J is exhausted to the low temperature reservoir, how much work does the engine do?

.462.0K650K 35011

H

Cr =−=−=

TTe(a) The maximum possible efficiency is

The engine operates at e = 0.65er = 0.30 or 30% efficiency.

( )kJ 7.2

11 CCC

CHnet

=⎟⎠

⎞⎜⎝

⎛−

=−−

=

−=

QeeQ

eQ

QQW

( ) .1 HC QeQ −=

(b) The heats exchanged at the reservoirs are related to each other through