Thermodynamics

How Energy Is Transferred As Heat and Work

Animation Courtesy of Louis Moore

How Internal Energy can Increase

Heat can be added (Symbol Q)Mechanical Work can be done on the system(like a piston compressing gas)

(Symbol W)

The First Law

U = Q + W U is internal energy +Q is heat added (absorbed) +W is net work done on system

The first law is a restatement of the law of conservation of energy

-

Piston and Cylinder

Sign Conventions

U = Q + W Work done on system is positive Heat leaving system is negative

Implication: When U = 0, Q = -W

Reminder: U = 3/2nRT = 3/2 NkT

Examples

(1) 1000 J of heat is added to the system and 500 j of work is done on the system. What is the change of internal energy?

(2) 300 J of heat escapes and 200 J of work is done by the system. What is the change of internal energy?

Answer: 1500 J

Answer: -500 J

Processes

1. Isothermal (no temperature change)T = U = 0 ; PV = constant2. Adiabatic (no heat flow in or out) Q = 0

3. Isobaric (no change in pressure)4. Isochoric (no change in volume)

PV Diagram for Isothermal Process

T = U = 0

Adiabatic Processes

No heat added or taken awayExamples: Quickly pushing down a bicycle pump Compression stroke in heat engine Expansion in power stroke

Why adiabatic – too fast for any appreciable heat to enter or leaveAlso if well insulated

PV Diagram for Adiabatic Process

Q = 0

Happens when system is well insulated or if process happens very quickly as in rapid expansion of gases in an internal combustion engine.

Expansions or Compressions?

If Q = 0 is U positive or negative? What about the temperature?

Compression, since V decreases

U and T positive

PV Diagram for Isochoric Process

What does the PV Diagram look like for an Isobaric process?

P

V

What happens in compression stroke of an engine?

Adiabatic since fastWork is done ON gasU increases since U = 0 + (W)T increasesIn diesel fuel-air

mixture ignites spontaneously

Work

If pressure constant W = -Fd = -PAd = -PVWork negative if expansionWork positive if compression

Remember new convention: work done ON is positive

Calculating Work P V

Work done by a gas equals area under PV curve

FIND THE WORK! Hint: 1 atm = 105 N/m2 ; 1l = 10-3 m3

Answer: About 250 Joules

Work Along a Curved Path

Use calculus or graph paper to estimate

Work Around a Closed Path

Equals area enclosed on PV diagramNegative for clockwise pathPositive for counter-clockwise path

First Law Example

An ideal gas is slowly compressed at constant pressure of 2.0 atm from 10L to 2L. With volume constant heat is added; pressure and temperature rise until temperature reaches its initial value.Find total work done on gas

Find total heat flow into gas

Find net change in U?

P

V

2atm

+1600 J

-1600 J

zero, since returns to initial value

How a Car Engine Works

LINK TO “HOW STUFF WORKS”

Work Done in an Engine

0.25 moles of gas expands quickly and adiabatically against piston. T drops from 1150 k to 400K How much work is done?Hint: use U = Uf – Ui = 3/2nR(Tf – Ti)

Answer: 2300 J

Second Law of Thermodynamics

Heat flows naturally from hot to cold objectsNo device can simply transform heat to work(100% efficient engine impossible)A perfect refrigerator is impossibleThe total entropy(disorder) of a system and its environment increases in natural processes

Heat Engines

Heat input Q1 at a high temperature is partly transformed into work W. The waste heat Q2 is exhausted at a lower temperature

QH

W

QL

QH = W + QL Efficiency = W/QH

Carnot Engine: most efficient(ideal)

Efficiency

= useful work/ QH = W/ QH = (QH-QL)/QH

QH = W + QL ;QH is at operating temperature

Eff = 1 – QL/QH ; QL is exhaust heat

Eff ideal = 1 – TL/TH for Carnot EngineKelvin temperatures only

Examples

In one cycle of an engine 5000 j are released by burning and 3000 j are exhausted. What is efficiency?Eff = W/QH = 2/5

An ideal engine operates between 900 and 500 degrees. Find efficiencyEff = 1 – TL/TH = 4/9

Heat Engine Facts

Gasoline engines operate at 15-25% efficiencyDiesel engines operate at 30-50%. They operate at higher temperaturesMany other engine designs exist such as Sterling engine

Refrigerator

Heat engine operated in reverse

Q: Will your kitchen be hotter or colder with the refrigerator door open?

CP = Q2/W =

Q2/(Q1-Q2)

Coefficient of performance

W is work done by motor/compressor

Entropy

Change in entropy S of a system when heat Q is added to it is

S = Q/TAccording to Second Law of

Thermodynamics, the entropy of an isolated system never decreases.

Entropy Examples

Molecules do not migrate to one corner of roomDropped cup breaks; pieces do not spontaneously reassemble themselvesHammer hitting nail heats it. Hammer on top of nail does not spontaneously rise up as nail coolsMixtures do not separate by themselves

Heat Death

In any natural process some energy becomes unavailable to do useful workEnergy is degradedGoes from most orderly form (mechanical) to least orderly (heat)Eventually all energy of universe is degraded to heat; all change ceases