Chapter 14Chapter 14

Introduction To Introduction To ThermodynamicsThermodynamics

ThermodynamicsThermodynamics

Study processes where energy is Study processes where energy is transferred as heat, worktransferred as heat, work

Heat: transfer energy due to Heat: transfer energy due to TT00 Work: transfer energy when Work: transfer energy when T=0T=0

Zeroth Law of ThermodynamicsZeroth Law of Thermodynamics

If objects A and B are separately in If objects A and B are separately in thermal equilibrium with a third object, C, thermal equilibrium with a third object, C, then A and B are in thermal equilibrium then A and B are in thermal equilibrium with each other.with each other.

Allows a definition of temperatureAllows a definition of temperature

Internal EnergyInternal Energy

Internal EnergyInternal Energy, U, is the energy , U, is the energy associated with the microscopic associated with the microscopic components of the systemcomponents of the system• Includes kinetic and potential energy Includes kinetic and potential energy

associated with the random associated with the random translational, rotational and vibrational translational, rotational and vibrational motion of the atoms or moleculesmotion of the atoms or molecules

• Also includes any potential energy Also includes any potential energy bonding the particles togetherbonding the particles together

Gas as ExampleGas as Example

In a monatomic gas, the KE is the In a monatomic gas, the KE is the only type of energy the molecules only type of energy the molecules can havecan have

RTM

mU )(

2

3

First Law of ThermodynamicsFirst Law of Thermodynamics

The First Law of Thermodynamics The First Law of Thermodynamics tells us that the internal energy of a tells us that the internal energy of a system can be increased bysystem can be increased by• Adding energy to the systemAdding energy to the system• Doing work on the systemDoing work on the system

There are many processes through There are many processes through which these could be accomplishedwhich these could be accomplished• As long as energy is conservedAs long as energy is conserved

First Law of ThermodynamicsFirst Law of Thermodynamics

Energy conservation lawEnergy conservation law Relates changes in internal energy to Relates changes in internal energy to

energy transfers due to heat and energy transfers due to heat and workwork

Applicable to all types of processesApplicable to all types of processes Provides a connection between Provides a connection between

microscopic and macroscopic worldsmicroscopic and macroscopic worlds

First Law, cont.First Law, cont.

Energy transfers occur due toEnergy transfers occur due to• By doing workBy doing work

Requires a macroscopic displacement of Requires a macroscopic displacement of an object through the application of a an object through the application of a forceforce

• By heatBy heat Occurs through the random molecular Occurs through the random molecular

collisionscollisions Both result in a change in the Both result in a change in the

internal energy, internal energy, U, of the systemU, of the system

First Law, EquationFirst Law, Equation

If a system undergoes a change from If a system undergoes a change from an initial state to a final state, then an initial state to a final state, then U = UU = Uff – U – Uii = = Q - WQ - W• Q is the energy transferred to the Q is the energy transferred to the

system by heatsystem by heat• W is the work done by the systemW is the work done by the system• U is the change in internal energyU is the change in internal energy

First Law – Signs First Law – Signs

Signs of the terms in the equationSigns of the terms in the equation QQ

Positive if energy is transferred Positive if energy is transferred toto the system by heat the system by heat Negative if energy is transferred Negative if energy is transferred out ofout of the system by the system by

heatheat

• WW Positive if work is done by the systemPositive if work is done by the system Negative if work is done on the systemNegative if work is done on the system

• UU Positive if the temperature increasesPositive if the temperature increases Negative if the temperature decreasesNegative if the temperature decreases

Results of Results of UU

Changes in the internal energy result Changes in the internal energy result in changes in the measurable in changes in the measurable macroscopic variables of the systemmacroscopic variables of the system• These includeThese include

PressurePressure TemperatureTemperature VolumeVolume

Notes About WorkNotes About Work

Positive work decreases the internal Positive work decreases the internal energy of the systemenergy of the system

Negative work increases the internal Negative work increases the internal energy of the systemenergy of the system

This is consistent with the definition This is consistent with the definition of mechanical workof mechanical work

Second Law of Second Law of ThermodynamicsThermodynamics

Heat flows naturally from hot to Heat flows naturally from hot to cold objects. Heat will not flow cold objects. Heat will not flow spontaneously from cold object to spontaneously from cold object to hot object.hot object.

Work in Thermodynamic Work in Thermodynamic Processes – AssumptionsProcesses – Assumptions

Dealing with a gasDealing with a gas Assumed to be in thermodynamic Assumed to be in thermodynamic

equilibriumequilibrium• Every part of the gas is at the same Every part of the gas is at the same

temperaturetemperature• Every part of the gas is at the same Every part of the gas is at the same

pressurepressure Ideal gas law appliesIdeal gas law applies

Work in a Gas CylinderWork in a Gas Cylinder

The gas is contained in a The gas is contained in a cylinder with a moveable cylinder with a moveable pistonpiston

The gas occupies a volume V The gas occupies a volume V and exerts pressure P on the and exerts pressure P on the walls of the cylinder and on walls of the cylinder and on the pistonthe piston

Work done by the gas Work done by the gas expandingexpanding

VPW

ExampleExample

Work done by expanding gasWork done by expanding gas

More about Work on a Gas More about Work on a Gas CylinderCylinder

When the gas is allowed to expandWhen the gas is allowed to expand• ΔV is positive ΔV is positive • The work done by the gas is positiveThe work done by the gas is positive

When the gas is compressedWhen the gas is compressed• ΔV is negativeΔV is negative• The work done by the gas is negativeThe work done by the gas is negative

When the volume remains constantWhen the volume remains constant• No work is done by the gasNo work is done by the gas

First Law, EquationFirst Law, EquationVPUQ

Types of Thermal ProcessesTypes of Thermal Processes

IsochoricIsochoric• Volume stays constant(Volume stays constant(V=0)V=0)• No work done by the systemNo work done by the system

IsothermalIsothermal• Temperature stays the sameTemperature stays the same• No change of internal energyNo change of internal energy

AdiabaticAdiabatic• No heat is exchanged with the No heat is exchanged with the

surroundingssurroundings

UQ

VPQ

VPU 0

P-V diagramP-V diagram

Heat EngineHeat Engine

A heat engine takes in energy by A heat engine takes in energy by heat and partially converts it to other heat and partially converts it to other formsforms

In general, a heat engine carries In general, a heat engine carries some working substance through a some working substance through a cyclic processcyclic process

Turn heat into workTurn heat into work0U

WQQWQ outin

Heat Engine, cont.Heat Engine, cont.

Energy is transferred Energy is transferred from a source at a from a source at a high temperature high temperature (Q(Qhh== QQinin))

Work is done by the Work is done by the engine (Wengine (Wengeng=W)=W)

Energy is expelled to Energy is expelled to a source at a lower a source at a lower temperature temperature (Q(Qcc==QQoutout))

Thermal Efficiency of a Heat Thermal Efficiency of a Heat EngineEngine

Thermal efficiency is defined as the ratio Thermal efficiency is defined as the ratio of the work done by the engine to the of the work done by the engine to the energy absorbed at the higher energy absorbed at the higher temperaturetemperature

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

in

out

in

outin

in Q

Q

Q

QQ

Q

We

1

Maximum efficiencyMaximum efficiency Most efficient engine is Carnot engineMost efficient engine is Carnot engine Depends only on the temperature of the hot Depends only on the temperature of the hot

and cold sources.and cold sources.

TTH H and Tand TLL are in Kelvin are in Kelvin Carnot CycleCarnot Cycle

H

L

T

Te

1

inputheat

outputwork efficiency max

max

Sadi CarnotSadi Carnot

1796 – 18321796 – 1832 French EngineerFrench Engineer Founder of the Founder of the

science of science of thermodynamicsthermodynamics

First to recognize First to recognize the relationship the relationship between work and between work and heatheat

Carnot EngineCarnot Engine

A theoretical engine developed by Sadi A theoretical engine developed by Sadi CarnotCarnot

A heat engine operating in an ideal, A heat engine operating in an ideal, reversible cycle (now called a reversible cycle (now called a Carnot Carnot CycleCycle) between two reservoirs is the most ) between two reservoirs is the most efficient engine possibleefficient engine possible

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

Carnot CycleCarnot Cycle

ExampleExample

A heat engine works between 400 C A heat engine works between 400 C and 200 C. What is its maximum and 200 C. What is its maximum efficiency? If the engine uses 10Mcal efficiency? If the engine uses 10Mcal in a hour and operates at maximum in a hour and operates at maximum efficiency, what is the work output? efficiency, what is the work output? Power output? How about at 80% of Power output? How about at 80% of maximum efficiency?maximum efficiency?

Heat Pumps and RefrigeratorsHeat Pumps and Refrigerators

Heat engines can run in reverseHeat engines can run in reverse• Energy is injectedEnergy is injected• Energy is extracted from the cold reservoirEnergy is extracted from the cold reservoir• Energy is transferred to the hot reservoirEnergy is transferred to the hot reservoir

This process means the heat engine is This process means the heat engine is running as a heat pumprunning as a heat pump• A refrigerator is a common type of heat A refrigerator is a common type of heat

pumppump• An air conditioner is another example of a An air conditioner is another example of a

heat pumpheat pump

Heat Pump, contHeat Pump, cont

The work is what The work is what you pay foryou pay for

The QThe Qcc is the is the desired benefitdesired benefit

The coefficient of The coefficient of performance (COP) performance (COP) measures the measures the performance of the performance of the heat pump running heat pump running in cooling modein cooling mode

Heat Pump, COPHeat Pump, COP

In cooling mode,In cooling mode,

The higher the number, the betterThe higher the number, the better A good refrigerator or air conditioner A good refrigerator or air conditioner

typically has a COP of 5 or 6typically has a COP of 5 or 6

LH

L

TT

TCOP

max

W

QCOP C ||

Heat Pump, COPHeat Pump, COP

In heating mode,In heating mode,

The heat pump warms the inside of The heat pump warms the inside of the house by extracting heat from the house by extracting heat from the colder outside airthe colder outside air

Typical values are greater than one Typical values are greater than one

LH

H

TT

TCOP

max

W

QCOP H ||

ExampleExample

A gasoline engine takes in 2500 J of A gasoline engine takes in 2500 J of heat and delivers 500 J of mechanical heat and delivers 500 J of mechanical work per cycle. Heat is obtained by work per cycle. Heat is obtained by burning gasoline with a heat of burning gasoline with a heat of combustion of 5.0x10^4 J/g. combustion of 5.0x10^4 J/g. Determine thermal efficiency, heat Determine thermal efficiency, heat lost, gas used during each cycle, lost, gas used during each cycle, power output with 100 cycles/s, power output with 100 cycles/s, amount of gasoline used in one hour.amount of gasoline used in one hour.