ConservationConservation

Work ExpandedWork Expanded

Mechanical work involves a Mechanical work involves a force acting through a force acting through a distance.distance.

Work can involve a change Work can involve a change in internal energy.in internal energy.• Temperature may changeTemperature may change

• Temperature did not cause Temperature did not cause the workthe work

Work is an energy transfer that is not due to a temperature difference.

Heat is an energy transfer that is due to a temperature difference.

First Law of First Law of ThermodynamicsThermodynamics

Internal energy can only change by heat transferred Internal energy can only change by heat transferred to and work done by a system.to and work done by a system.• Heat added is +Heat added is +• Heat lost is –Heat lost is –• Work by a system is +Work by a system is +• Work on a system is -Work on a system is -

WQU

When work is defined as positive on a system it is U = Q + W.

PV DiagramPV Diagram

The ideal gas law links The ideal gas law links pressure, volume, and pressure, volume, and temperature. temperature. • PVPV = = nRTnRT

For fixed quantity of gas, any For fixed quantity of gas, any two of the three determine two of the three determine the third.the third.

Graph of pressure vs volume Graph of pressure vs volume describes the system.describes the system.

P

V

111 ,, TVP

222 ,, TVP

Slow MotionSlow Motion

During rapid change the During rapid change the macroscopic state variables macroscopic state variables are not well defined.are not well defined.

On a PV diagram it is On a PV diagram it is assumed that the system assumed that the system changes slowly.changes slowly.

This is a This is a quasi-staticquasi-static change. change.

Measuring WorkMeasuring Work

The mechanical work can be The mechanical work can be measured on the PV measured on the PV diagram.diagram.

The work done is the area The work done is the area under the PV curve under the PV curve describing the system.describing the system.

P

V

111 ,, TVP

222 ,, TVP

VPW

xPAW

xFW

work done

Constant TemperatureConstant Temperature

Changes often involve Changes often involve holding one variable holding one variable constant.constant.

Moving a piston slowly Moving a piston slowly changes pressure and changes pressure and volume.volume.

Temperature remains the Temperature remains the same.same.

Base is kept at a constant temperature

Walls and top are insulating

Isothermal ProcessIsothermal Process

For an ideal gas at constant For an ideal gas at constant temperature temperature TT = 0, = 0, PP is is inversely proportional to inversely proportional to VV..• PP = = nRTnRT((1/V1/V))

The work done by an ideal The work done by an ideal gas can be found with gas can be found with calculus.calculus.

P

V

TVP ,, 11

TVP ,, 22

1

2lnV

VnRTW

Internal Energy ConservedInternal Energy Conserved

An ideal gas only changes An ideal gas only changes internal energy with internal energy with temperature change.temperature change.• UU = 0 = 0

From the first law, work done From the first law, work done equals heat flow.equals heat flow.• UU = = QQ – – WW

• QQ = = WWHeat flow into gas

Work done by gas

UnderwaterUnderwater

A scuba diver is swimming at A scuba diver is swimming at a depth of 25 m where the a depth of 25 m where the pressure is 3.5 atm. The pressure is 3.5 atm. The exhaled air forms bubbles exhaled air forms bubbles 8.0 mm in radius. The 8.0 mm in radius. The bubbles stay at 300 K as bubbles stay at 300 K as they rise.they rise.

How much work is done by How much work is done by each bubble as it expands each bubble as it expands reaching the surface?reaching the surface?

The ideal gas law is used to The ideal gas law is used to find the amount of gas.find the amount of gas.

P and V are related.P and V are related.

This is an isothermal This is an isothermal process.process.

W = 0.95 J.W = 0.95 J.

next

2

11

313

4 lnP

PPrW

)( 334 rPPVnRT

2211 VPVP