Temperature & Heat

Kinetic Molecular Theory• Matter is composed of tiny particles– Atoms– Molecules

• The particles of matter are in constant random motion– Gas: random velocities and collisions– Liquid: particles move and vibrate

while remaining in contact with other particles

– Solid: particles vibrate in place (their relative positions remain fixed)

Temperature• Temperature is a measure of how hot or cold

an object is, but what is it in terms of KMT?• Temperature is a measure of the average

kinetic energy of the particles in a substance– Since every atom or molecule is moving or

vibrating, it has kinetic energy– Temperature is a measure of the average kinetic

energy that each particle has– Temperature by itself gives no information about

how much total energy is present in the substance

Thermal Energy• Thermal energy is the total kinetic energy of

the particles in a substance– Loosely speaking, thermal energy is “heat energy”

• We measure thermal energy by keeping track of changes in internal energy, U

U = total energy in a system of particles = thermal energy + chemical energy + nuclear

energy

• A change in the thermal energy results in a change in internal energy, U

• The unit for internal energy is the joule, J

Heat• Heat is the transfer of thermal energy from

one object (substance, body) to another due to a temperature difference

– Object A loses energy while Object B gains energy• Heat is represented by the symbol Q• Heat, like thermal energy, has units of joules (J)

heat (Q)

Object A Object B

TA TB

TA > TB

Heat & Internal Energy• If an object absorbs heat (and no work is

done), its internal energy increases

• Likewise, if an object releases heat (and no work is done), its internal energy decreases

UQ U increases

U > 0

UQU decreases

U < 0

Direction of Heat & Thermal Equilibrium

• Heat requires a temperature difference• Heat flows spontaneously from hotter objects to

colder ones (higher temp. to lower temp.)• Temperature tells us whether heat transfer can

or cannot occur:– Yes it can, if there is a temperature difference– No it can’t, if there is no temperature difference

• If two objects are at the same temperature, they are in thermal equilibrium – Objects in thermal equilibrium cannot transfer heat

Zeroth Law of Thermodynamics• The Zeroth Law of Thermodynamics says:

If two bodies are in thermal equilibrium with a third body, they are in thermal equilibrium with each other– The zeroth law ensures that temperature is a

useful physical quantity– Without the zeroth law, temperature would not be

able to predict heat transfer• The physicist James Clerk Maxwell expressed

this law as “All heat is of the same kind”

Temperature Measurement• A thermometer is a device that

measures temperature• The classic mercury (or alcohol)

thermometer uses two spontaneous processes:– The “bulb” of the thermometer (which

contains most of the mercury) is placed in contact with an object and allowed to reach thermal equilibrium with it

– Thermal expansion/contraction of the very thin column of mercury above the bulb indicates the temperature in degrees

scale

bulb

column

glass

Temperature Scales• There are three temperature scales:– Fahrenheit (F)– Celsius (C)– Kelvin (K)

• To convert Celsius to Fahrenheit:TF = (9/5)TC + 32.0

• To convert Fahrenheit to Celsius:TC = (5/9)(TF 32.0)

• To convert Celsius to KelvinT = TC + 273.15

Water Freezes Water BoilsFahrenheit 32F 212FCelsius 0C 100CKelvin 273.15 K 373.15 K

Comparison of the Temp Scales:

Absolute Zero• Absolute zero is the name for the lowest

possible temperature• For a substance at absolute zero:– the particles cease to move– the thermal energy content is zero– the temperature, in Kelvin, is zero

• Nothing in the universe is ever at absolute zero– Absolute zero is a theoretical state determined by

extrapolation– Scientists have brought very small quantities to

temperatures less than 2 10-7 K

The Kelvin Scale• The Kelvin scale is the scientific temperature

scale used in thermodynamics– The kelvin (K) is the unit of temperature– 0 K corresponds to absolute zero– The temperature steps in Kelvin are the same as

the steps in Celsius: Tkelvin = Tcelsius

• When measured using the Kelvin scale, temperature becomes a true physical quantity– The thermal energy in a gas (U) is proportional to

the temperature in kelvin (T):U T (true only for kelvin)

Types of Heat Transfer• There are three primary types of heat transfer:– Conduction– Convection– Radiation

• Conduction is heat transfer within an object or between objects when they are touching

• Convection is when heat is carried from one place to another by a fluid

• Radiation is heat transfer by electromagnetic radiation (light, infrared, microwaves, etc.)

T1 T2H

L

A

Conduction• Conduction in a material happens when there is

a temperature gradient in the material

• The rate of heat transfer, H, in watts, is given by H = Q/t = kA(T1 T2)/L

– k is the thermal conductivity of the material with units of W/(mC) = W/(mK)

– A is the cross-sectional area (m2), L is the length (m)

T1 > T2

Example Conduction ProblemAn aluminum rod of length 30.0 cm and diameter 1.5 cm has a temperature of 85 C at one end and 18 C at the other. What is the rate of heat flow through the rod?k (Al) = 210 W/(mK)A = d2/4 = (.015 m)2/4 = 1.77 10-4 m2

H = kA(T1 T2)/L

= (210 W/mK)(1.77 10-4 m2)(8518C)/(0.30m)= 8.3 W

Thermal Expansion• Most substances expand when heated and

contract when cooled

• The amount of expansion or contraction (L) depends on the material and is proportional to the change in temperature T:

L = L0T– is the linear coefficient of thermal expansion for

the material (units of K-1)

L0

L

L

Example Thermal Expansion Problem

An aluminum rod of length 30.0 cm and diameter 1.5 cm increases in temperature by 95 C. How much does the length of the rod increase?a(Al) = 23 10-6 K-1 L = L0T

= (23 10-6 K-1)(30.0 cm)(95 K)= 0.066 cm= 6.6 10-4 m

Specific Heat• The specific heat of a substance is the amount

of energy required to change the temperature of 1 kg of that substance by 1C

• Specific heat is denoted by “cP”• Specific heat has units of J/kgC• Specific heat equation:

Q = cPmT = cPm(Tfinal Tinitial)

where Q is energy transferred as heat

Example• How much energy must be transferred as heat

to raise the temperature of 0.75 kg of water from 18C to 100 C?T = 100 C 18 C = 82Cm = 0.75 kgcP = 4186 J/kgC

Q = (4186 J/kgC)(0.75 kg)(82C) = 260 000 J = 260 kJ

Example

• What is the specific heat of a 75.0-g piece of metal that releases 1850 J of heat while cooling from 98.6 C to 24.3 C?

m = 0.0750 kgQ = -1850 JT = 24.3 C – 98.6 C = -74.3 C cp = Q/(m·T)

= (-1850 J)/(0.0750 kg)/(-74.3 C ) = 332 J/(kg·C)

Table of Specific HeatsMaterial Specific heat

J/(kgC)

aluminum 903

brass 376

copper 385

iron 450

zinc 388

silver 235

lead 130

water 4186

Calorimetry• A calorimeter is a device used to

measure the specific heat of a substance

• A test substance is heated and placed in the water

• The amount of heat the water absorbs is Qw = cPwmwTw

• The amount of heat the substance releases is Qx = cPxmxTx

• But Qx = -Qw

• So cPx = -Qw/mxTx