Slide 1

PHY1039Properties of MatterFirst Law of Thermodynamics and Heat Capacity (See Finns Thermal Physics, Ch. 3)

March 5 and 8, 2012

Lectures 9 and 10Internal Energy, UDefinition: The internal energy is the total energy of a system, equal to the sum of the kinetic and potential energies of its constituent atoms/molecules.Gases and liquids

Kinetic energy:Translational motion with a velocity n.RotationMolecular vibrationnynznnxTranslational energy

Rotational energy of a diatomic molecule, e.g. N2, O2, H2Kinetic Energy of Gas MoleculesFigure from Understanding Properties of Matter by M. de PodestaRotational energy of a non-linear triatomic molecule, e.g. H2OFigure from P. Atkins The Elements of Physical Chemistry

Three degrees of freedom (one for each type of rotation)

Symmetric and anti-symmetric stretching vibration

Bending vibrationVibrational Energy of Gas MoleculesResonant frequency for a stretching vibration of an N2 molecule is on the order of 1013 Hz. Spring constant K is about 100 N/m.Modes of Vibration in Triatomic MoleculeNNKinetic Energy:Molecular vibration in x, y and z directions

Internal Energy of SolidsroPotential Energy:Varies with distance between molecules (analogy to stretching a spring)

Three degrees of freedomThree degrees of freedom (one in each direction)

Internal Energy, UInternal energy depends on the state of a system through the state variables: U = U(P, V, T).We call U a state function because it depends on the state of the system.DU12 will always take the same value, regardless of the path, in going from 1 to 2. The difference in value of the state functions for two different states is said to be path independent.U1U2PVConsider two different states of a system: 1 and 2.

The difference in the internal energy between the two states is:

Change in Internal Energy, DU in an Adiabatic ProcessAdiabatic work on a system takes it from State 1 to State 2.Area under the PV curve determines the amount of work done (value is path dependent)Adiabatic work changes the internal energy of the system by DU. For the two states, DU is fixed and hence there can be only one adiabatic path between States 1 and 2.12PVAdiabatic wallFNon-Adiabatic Path12PV2What is Now consider an alternative, non-adiabatic path from 1 to 2 via 2.DU12 must be the same (it is path independent) as before, but W122 is different than on the adiabatic path.First Law of ThermodynamicsHeat, Q, is the difference between DU and W:Q = DU W The First Law of Thermodynamics is usually stated as:DU = Q + WDifferential form of First Law: dU = dQ + dWSign convention:Heat into system: +ve QHeat out of system: -ve QUnits of U, Q and W are Nm (or Joules, J)The First Law is a balance sheet of energy. It tells us that heat into and work on a system raises its internal energy. If a system does work on its surroundings or gives off heat, then its internal energy decreases.Heat, QHeat is the non-mechanical exchange of energy between a closed system and its surroundings. Heat flows spontaneously across a diathermal wall when two systems at different temperatures are in contact.In contrast, work acts in a specific direction: pushing atoms together or pulling them further apart.

F

HotterColderHeat is energy in motion that moves across the system wall. Heat is stored in the system as internal energy.

Mechanisms of Heat Exchange between System and Surroundings

Thermal radiation: emission of electromagnetic radiationConduction: carried by molecular vibrationshotcoldConvection: carried by molecular transport from one position to another

Radiation energy densityPlanck distribution law

infraredUV-Vis.Spectral Distribution of Thermal RadiationEffective temperature of the Sun is 5780 K UV-visible radiation.

Internal Energy Change in a Cycle12PV3In a cycle, the system goes to other states and then returns to its original state.The change in internal energy at the end of the cycle is 0.

DU1231 = 0

DU1321 = 0Path Independence of Internal Energy Change The sign of DU depends on the direction of the path (i.e. which are the original and final states?).12PV3DU12 = DU132DU12 = DU132 = -DU21 = - DU231

Meaning of the First Law(1) Work can be converted into heat or heat can be converted into work in a process when there is no change in the internal energy. DU = 0 = Q + WW = - Q (remembering the sign convention!) If the state variables return to their original position after a process, then DU = 0.(2) Adiabatic work can raise the internal energy of a system, and hence raise its temperature.Q = 0, so that DU = WExamples of mechanical work include compressing a gas, stretching a wire or member, stirring a paddle in a viscous liquid.http://www.sil.si.edu/imagegalaxy/imagegalaxy_imageDetail.cfm?id_image=3087

In the 19th century, it was believed that systems contained a finite amount of heat. Particles of heat, called caloric, were thought to flow from hot to cold objects.Matter was thought to possess a finite amount of heat.Benjamin Thompson (Count Romford), a British soldier, observed that when boring tools did frictional work on cannons, there was a build-up of heat enough to boil water.He reasoned that work on a system can be given off to the surroundings as heat. Mechanical Equivalence of HeatAdiabatic Work, W, on the system:Internal Energy, U, increases: T rises

Joules Paddle Experiment

1840 - 494.2 Nm of Work raised the T of 1 g of water by 1 K = 4.2 J = 1 calorie4.2 Nm of adiabatic work on the water is equivalent to 4.2 Nm of heat into the water in raising the internal energy.

What was the significance of 772.55 to James Joule?(Discuss in SGT)The tomb of James Joule

http://www.shivaranjan.com/2006/08/22/irish-company-claims-creation-of-perpetual-motion-machine/

http://theseep.wordpress.com/2008/02/10/could-perepiteia-perpetual-motion-machine-be-the-real-deal/http://www.todayinsci.com/Books/MechApp/chap23/page28.htmAre perpetual motion machines possible?W = DU - Q Continuous work on surroundings (-ve W) requires the continual input of heat (+ve Q) or removal of internal energy (which is finite!)VPTwo Types of Heat CapacityIsochoric ProcessIsobaric ProcessT1T2VPT1T2(V1, P1)(V1, P2)P1P2V1V2T2 > T1T2 > T1V1P1(V1, P1)(V2, P1)Molar Heat Capacity, CP, of the Elements at 298 K

Figure from Understanding Properties of Matter by M. de PodestaMolar Heat Capacity, CP, of Monoatomic and Diatomic Gases

Figures from Understanding Properties of Matter by M. de PodestaDiatomic GasMonoatomic Gas