Lec 1 - Temperature and Heat

7/27/2019 Lec 1 - Temperature and Heat

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Text Books for the Course

UP-201: Thermal and Modern Physics

1. Serway and Jewitt,Physics for Scientists and Engineers

with Modern Physics (7th Edition)

2. Young and Friedman, University Physics with Modern

Physics (12th Edition) 3. Halliday, Resnick and Walker,Fundamentals of

Physics, Extended(8th Edition)

4. Kenneth Krane, Modern Physics, Second Edition

5. OpenstaxCollege Physics - available free at

http://cnx.org/content/col11406/1.7

All of the first four are available in cheap Indian / Asian

Editions, and the last one is a free e-book

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U-P 201 Lec 1:

Thermal Physics: Some Basic Notions

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What is thermal physics

Atomic hypothesis and Internal Energy

Ideal gas and State variables

Systems in mechanical contact

Systems in thermal contact, Heat, Thermal Equilibrium,,Temperature

The zeroth law of thermodynamics

Measurement of Temperature and other state variables

Celsius and Fahrenheit Scales

Constant volume gas thermometer and the Absolute or

Kelvin scale

Ranges of Temperature in Nature


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What is Thermal Physics

We all have intuitive notions of "hot" and "cold,

of "temperature", the degree of "hotness" or "coldness "

based primarily on our sense of touch.

Our senses, and hence these intuitive notions are somewhat

imprecise.

Examples

Sticking one hand in hot water, another in cold water and both in

tepid water

A conducting object feels cold to touch where as an insulating objectat the same temperature does not.

Years ( > 2oo) of careful experimentation and rational analysis

have led to a near complete and precise understanding of these and

related notions and phenomena => The subject ofthermal physics,

the subject of the next few lectures OCP Section 13.1

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Atomic Hypothesis and Internal Energy

crucial under pinning => the "atomic hypothesis: all things

are made of atoms - tiny little particles that move around in

perpetual motion, attracting each other when they are a little

distance apart, but repelling upon being squeezed into one

another, [From Feynman Lectures Vol. I, section 1.2). Systems to which thermal physics applies typically have very

large numbers (~1020 or more) of atoms

=> Thermal Systems

The Internal or Thermal energy U of a system is the energy

of its internal constituent degrees of freedom (normally

atoms, but in metals, ions + electrons...) apart from its overall

(centre of mass) translational and rotational Kinetic energy.

OCP Section 13.1

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Ideal Gas

The simplest example of a thermal system, which we will

keep using for illustrative purposes, is a "mono-atomic

ideal gas " ofN rare-gas atoms contained in a volume V

large enough that the consequently large typical inter-

atomic distances allow us to neglect inter-atomic potentialenergies

i.e., the internal energy U is just

the Kinetic energy

212

1

2 2 212

1

( )

N

i

i

N

ix iy iz

i

U m

m v v v

v

OCP Section 13.1

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Ideal Gas and State Variables

The atoms that are running around also collide against andrebound off the walls of the container, giving rise to a

pressure P = (Average) Force / (Unit Area).

P, U, Vare examples of State variables characterizing

the Thermal, or Thermodynamic, orMacro state of thesystem, as distinct from the manymicro-states of the

system which can correspond to the same macro-state

In a later lecture (Kinetic Theory of Gases) we will see that

for the ideal monatomic gas

Example of an Equation of State

2

3

UP

V

OCP Section 13.1

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Systems in mechanical Contact

Two systems A and B which share a common flexible ormovable wall (eg. a movable piston of area ) are said to

be in mechanical contact.

IfPA = PB the two systems will be in mechanical

equilibrium. If, initially, it is known from experiment that

and until the two systems again have equal

pressures and attain mechanical equilibrium.

In this process work is done by system A on system B andsome internal energy is exchanged between the two

systems. As we will prove later

i i

A BP P ( , )A AP V

( , )B BP V

( ) ( )A A B A B BU P P dx P P dV U A

A

OCP Section 13.1

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Thermal Contact between Systems

Apart from such a mechanical route, three othermechanisms for the exchange of internal energies between

systems are known, namely conduction, convection and

radiation - together, such exchanges are known as heat

exchanges. (More about these mechanisms later.) When two systems A and B are such that heat exchanges

between them can take place readily, they are said to be in

thermal contact.

we also know ways of minimizing, and nearly eliminatingthe possibilities of heat exchanges between two systems.

Then the two are said to be thermally isolated from each

other

OCP Section 13.1

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Temperature and Thermal Equilibrium

We saw that the equality or otherwise of the state variable P

determines whether mechanical exchange of internal energies

does not or does take place

Experiments show that there exists another state variable, the

temperature, orT, whose equality or otherwisedetermines whether heat exchanges between two systems do

not or do take place.

Typically is a monotonic increasing as Uincreases and vice

versa. If two systems A and B with equal temperatures are

brought into thermal contact, These will be no heat exchange

between them - they are in thermal equilibrium.

A B

OCP Section 13.1

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Temperature, Heat, and the Zeroth Law

of Thermodynamics

On the other hand, experiments show that if

initially , and until the two

temperatures equalize and thermal equilibrium is attained

Thus heat is the exchange of internal energies that takesplace between systems when they are at different

temperatures and allowed to be in thermal contact

Our skin is sensitive not to temperature but to the rate of

transfer of heat across it. That and the above notions helpus to understand the examples discussed in the beginning!

The existence of a state variable called temperature is

sometimes stated differently, and referred to as the zeroth

law of thermodynamics

i i

A B

( , )A AU ( , )B BU

OCP Section 13.1

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The Zeroth Law of Thermodynam ics

I f bodies A and B are each in thermal

equil ibrium with a thi rd body T, then Aand B are in thermal equil ibrium with

each other.

Starting from this law, it is possible to make

a logical argument to prove the existenceof temperature as a state variable!

From Halliday, Resnick and Walker, Fundamentals of Physics OCP Section 13.1

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Summary: Temperature and Heat

Heat is the internal energy

exchanged between a

system and its

envir onment, or between

two systems, because of a

temperature dif ference that

exists between them.

From Halliday, Resnick and Walker, Fundamentals of Physics OCP Section 13.1

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Measuring State Variables

State variables Such as VolumeVandPressurePare directly and easily measurable.

Instruments for measuring Pressure, which is a

very important state variable are called

barometers The SI unit of pressure (force per unit area) is

the Pascal: 1 Pa = 1 N/m2.

Another common unit is the atm (atmospheric

pressure): 1 atm = 1.013 x 105

N/m2

. A pressure of 1 atm will push a mercury

column up by 76 cm.

0P

0 HgP gh

h

Mercury Barometer

OCP Section 13.1

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Measuring Temperature

The internal energy, U being a sum over many (1020) variables isharder to measure directly

The temperature, T, is an even subtler state variable, and can be

measured only indirectly, but easily, because lots of other easily

measured properties of systems are affected by it.

Thus any reference system which has an observable, measurableproperty that changes substantially with its temperature becomes a

temperature sensor orthermoscope, and when properly calibrated, a

thermometer

Examples:

Volumes of liquids or gases at fixed pressure

The Dimensions of a solid

pressures of gases at fixed volume

resistance of metallic wires

the color (spectrum) of light (e-m radiation) emitted by an object

OCP Section 13.1

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Measuring Temperature In order to measure temperature we must:

Agree on a standard thermometer (method + device) against which allother thermometers can be calibrated.

Agree on a unit.

Agree on a standard reference point(s) to which we assign a certain

temperature.

The standard thermometer currently accepted is the constant

volume gas thermometer(Earlier, mercury or alcohol

thermometers)

The unit of temperature universally accepted now is the

Kelvin (K). (Earlier scales were Celsius and Fahrenheit)

The standard reference point is the triple point of water (T =

273.16 K or 0.01 C). (Earlier, freezing and boiling points of

water)

OCP Section 13.1

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Celsius and Fahrenheit Scales

Typically measured using expansionof mercury or alcohol confined to

capillary tubes

the Celsius scale:

0 is defined as the freezing point of

water. 100 is defined as the boiling point of

water.

the Fahrenheit scale:

0 was defined as the temperature of a

mixture of water, ice, and ammonium

chloride.

96 was as the temperature of the blood of

Fahrenheits wife.

Note: initially Fahrenheit divided his scale

in 12 segments; later he divided each

segment in 8 smaller segments

OCP Section 13.1

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The Celsiu s and Fahrenheit Scales

Limitations:

Alcohol Thermometers and mercury Thermometers do not agree far fromthe calibration points

Limited range (mercury Freezes below -39 C, alcohol boils above 85 C)

Melting and Boiling point of Water varies with variation of atmospheric

pressure, presence of impurities,

OCP Section 13.1

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The Cons tant Volume Gas Thermometer

consists of a bulb connected by a tube to a mercury

manometer filled with a dilute gas.

By raising and lowering reservoir, the mercury level in the

left arm of the U-tube is brought to the zero of the scale tokeep the gas volume constant.

The pressure exerted by the gas is then

The temperature of any body in thermal equilibrium with

the gas bulb is found to vary linearly with the pressure:

(B is a constant). Note that the pressure extrapolates to

zero at -273.15 C for all dilute gases!

0P P gh

273.15CT B P

Hence define a new Kelvin or Absolute

temperature scale (K) as

Such that P = 0 at 0 K for all dilute gases!

T = TC+273.15

OCP Section 13.1

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The Reference Temperature for the

Kelvin scale is the Triple Point ofwater measured using the triple

point cell

For thermal equilibrium between

the gas bulb and the triple-cell bulb

Therefore,

Finally, this works the best for very

small amounts of gas:

3 3 3273.16 273.15CT T B P

3

3

273.15CP

T T TP

0 3

(273.16 )gas

PT K lim

P

The Kelvin Temperature Scale

T3 = 273.16(Triple Point Temperature)

OCP Section 13.1

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Lec 1 - Temperature and Heat

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