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Chapter 13

Temperature and Kinetic Theory

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• Understand the difference between terms– Energy, energy transfer, change in energy– temperature, temperature change, temperature

difference• Internal energy of a substance (U) is the sum of

– the average kinetic energy (KE) of the molecules• related to temperature

– the potential energy of atoms and molecules• depends on their chemical bonding & phase state

(solid, liquid or vapor)

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4motion of particles

Internal Energy of Substance•Convenient model is that atoms vibrate as if connected by springs

• Kinetic energy as they oscillate

• Potential energy that keeps substance bound together as a solid, liquid or gas is similar to springs binding atoms and molecules together

internal energy

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Temperature is not heat • Temperature

– Kinetic Theory relates the motion of particles to their pressure, temperature and phase state

– proportional to the average KE per molecule– 2 scales used in science

• Celsius – measurements and heat calculations

• Kelvin – no negatives; used for ideal gas law calculations

6KE – temp relation

Celsius & Kelvin Temperature Scales

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13-3 Thermal Equilibrium and the Zeroth Law of Thermodynamics

Two objects placed in thermal contact will eventually come to the same temperature. When they do, we say they are in thermal equilibrium.

The zeroth law of thermodynamics says that if two objects are each in equilibrium with a third object, they are also in thermal equilibrium with each other.

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Expansion & Contraction• Most objects expand when their

temperature increases

• Linear thermal expansion depends on original length of rod and the temperature change

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Linear Thermal Expansion• The length L0 of an object changes by an

amount L when its temperature changes by an amount T

0L L T

• coefficient of linear thermal expansion

• T = (higher lower temp) not (final initial temp)

thermal expansion10

Linear Expansion Examples• Bimetallic strip

– two metal strips with different expansion coefficients welded together

• used as a temperature sensitive switch in electrical devices and appliances

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Expansion of Holes

• Hole in a solid object expands or contracts along with the object just as if it were filled with the material that surrounds it

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13-6 The Gas Laws and Absolute Temperature

The relationship between the volume, pressure, temperature, and mass of a gas is called an equation of state.

We will deal here with gases that are not too dense.

Boyle’s Law: the volume of a given amount of gas is inversely proportional to the pressure as long as the temperature is constant.

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13-6 The Gas Laws and Absolute Temperature

The volume is linearly proportional to the temperature, as long as the temperature is somewhat above the condensation point and the pressure is constant:

Finally P T when volume is constant14

13-7 The Ideal Gas Law

We can combine the three relations just derived into a single relation:

What about the amount of gas present? If the temperature and pressure are constant, the volume is proportional to the amount of gas:

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13-7 The Ideal Gas Law

We can now write the ideal gas law:

(13-3)

where n is the number of moles and R is the universal gas constant.

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13-8 Problem Solving with the Ideal Gas Law

Useful facts and definitions:

• Standard temperature and pressure (STP)

• Volume of 1 mol of an ideal gas is 22.4 L

• If the amount of gas does not change:

• Always measure T in kelvins

• P must be the absolute pressure = gas pressure + applied pressure from external source

17ideal gas law

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Pressure

2( )

Force NP Pascal Pa

Area m

Chapter 14

Heat

14-1 James Joule’s Experiment

If heat is a form of energy, it ought to be possible to equate it to other forms. The experiment below found the mechanical equivalent of heat by using the falling weight to heat the water:

Related the work done by the falling mass to the amount of energy transferred to the gas

Temperature of the gas increases as energy is transferred to it.

This energy transfer, when do to a temperature difference, is called heat.

Heat• Energy in transit from hot to cold

• Energy that flows from a higher temperature object to a lower temperature object due to the difference in their temperatures

• Units are Joules (J)

• Objects do not

contain heat, they

contain energy

heat21

Specific Heat Capacity c• The amount of heat Q required to

raise the temperature of a substance depends on– material property called specific heat

capacity c– the mass of the substance being heated m– the amount of temperature change T

Q cm T 22

Specific Heat Capacity c• The number of Joules required to change

the temperature of 1 kg of a substance by 1 oC

• units are

T = (higher lower temp) not (final initial temp)

o

Joules

kg C

Qcm T

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24specific heat capacity

Calorimetry• Determine of specific heat capacity using

temperature changes and • Cool object immersed in cup of hot water

• Conservation of energy principle states that heat lost by hot water equals heat gained by the object

• Q gain by cool = Q lost by hot

• Final equilibrium temperature of the system is reached when there is no more heat transfer from the water to the object

Q cm T

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Electric Heat Energy – current through a resistor

demo

Water vs Copper• Water

– very high specific heat capacity value • 4186 J/kgCo

– comes to a boil very slowly due to the large amount of heat (energy transfer) required to change its temperature

– conducts thermal energy at a slow rate

• Copper– much lower specific heat capacity=387 J/kgCo

– excellent thermal conductor due to the small amount of energy required to raise its temp. and metallic atomic structure transfers thermal energy rapidly

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Change of Phase• Heat that changes temperature of a substance

without changing its phase is calculated Q=mcT

• Once melting or boiling point is reached (when temp is increasing) then phase change begins

• Temperature stays constant during phase change

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Latent Heat of Fusion or Vaporization

• Heat required to melt 1 kg of a substance at its melting point = latent heat of fusion Lf

• Heat required to change the phase of 1 kg of a liquid to vapor (evaporation) at its boiling point = latent heat of vaporization Lv

• Number of Joules to melt or vaporize a substance Q = mLf or mLv

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•Evaporation is a cooling process – heat leaves with the vapor

Q added to solid increases KE of molecules

Q = mcT

Melting Point

Q added changes phase from all solid to all liquid

Q = mLF

temperature increases constant temperature

Q added to liquid increases KE of molecules

Q = mcT

temperature

increases

Boiling point

Q added changes phase from all liquid to all vapor

Q = mLv

constant temperature

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Heating Curve for Phase Change

Temperature stays constant during phase change

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Heat Energy (J)

Temp

(oC)

melting point

solid only

liquid only

vapor only

solid & liquid during phase change

Heating Curve for Phase Change

boiling point

liquid & vapor during phase change

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Heat Energy (J)

Temp

(oC)

solid changing temp

Q=mcT

liquid changing temp

Q=mcT

vapor changing temp

Q=mcT

liquid vaporizing into gas

Q=mLv

Total heat required to change phases

solid melting to liquid

Q=mLf

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Heat Transfer Mechanisms• 3 mechanisms of heat transfer• convection

– requires a material medium (matter)– motion of a fluid (liquid or vapor) due to temperature

difference

• conduction• requires a medium• through the material with no bulk motion of the

material as a result of temperature difference

• radiation• no medium required• electromagnetic waves transfer the heat energy

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14-6 Heat Transfer: Conduction

Heat conduction can be visualized as occurring through molecular collisions.

The heat flow per unit time is given by:

(14-4)

Conduction• molecules/atoms in the medium with large

amounts of kinetic energy (high temperature) collide with neighboring molecules/atoms

• metallic solids – excellent thermal and electrical conductors due to ability of free electrons to move through the material

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Diamond vs Copper• demonstration of thermal conductivity

differences

• diamond 7-8 times better thermal conductor than copper due to crystalline structure of carbon

• diamond’s thermal conductivity is higher than any other material

• cut ice with heat from hand

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14-7 Heat Transfer: ConvectionConvection occurs when heat flows by the mass movement of molecules from one place to another. It may be natural or forced; both these examples are natural convection.

Convection • higher temperature fluid (liquid or vapor)

expanding and rising

• lower temperature fluid falling into space vacated by rising warm fluid

• convection currents set up until temperature difference is eliminated

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41convection

14-8 Heat Transfer: Radiation

The most familiar example of radiation is our own Sun, which radiates at a temperature of almost 6000 K.

Radiation• Electromagnetic waves (also called

electromagnetic radiation) carry energy – different portions of electromagnetic spectrum

transfer heat• visible portion of spectrum = “light”• invisible portion of spectrum (infrared radiation)

microwaves are not “hot” – they cause food molecules to vibrate 43