It is a branch of physics that deals with

o the concept of heat,

o its relations with other forms of energy, and

o its roles in thermodynamic processes and phase changes.

Literally, THERMODYNAMICS means “power from heat”.

Direction of flow: hotter colder

Heat is a form of energy that flows from one system to another if the two systems are in thermal contact and are of not the same hotness.

What is HEAT?

It makes no sense to talk about the heat of a system – we can refer to heat only when energy is transferred as a result of hotness difference between two systems in thermal contact.

o Two systems are in thermal contact with each other when heat can be exchanged between them.

o When two systems are in thermal contact and there is no heat flow from one to another, the two systems are said to be in thermal equilibrium.

Definitions of thermal contact & thermal equilibrium

If object A and B are separately in thermal equilibrium with a third object C,

then object A and B are in thermal equilibriumwith each other.

The zeroth law of thermodynamics

Implication of the zeroth law of thermodynamics

There exists a scalar quantity called temperature, which is a property of all thermodynamics systems (in equilibrium states), such that temperature equality is a necessary and sufficient condition for thermal equilibrium.

Hence, the zeroth law allows us to define temperature, which can be used to determine whether an object is in thermal equilibrium with other objects.

The implication of the zeroth law of thermodynamics stated in the earlier slide is simple but not obvious.

The following analogy would help to understand it:

In a multi-lingual society, if any two persons A and B can separately communicate with a third person C, then A and B can communicate with each other.

This statement implies that there exist a language or method of communication which everyone in this society knows how to speak/use.

Another way to interpret the implication of the zeroth law of thermodynamics is as follows:

Whether two systems are in thermal equilibrium can be determined by means of a thermometer (temperature measuring device).

Thermometric properties and substances

o Any measurable physical property of a substance that varies with temperature can be used for temperature measurement. Such a property is often called a thermometric property.

o A substance with any thermometric property is call a thermometric substance.

Examples of thermometric properties:

o The volume of liquido The length of a solido The pressure of a gas at constant volumeo The volume of a gas at constant pressureo The resistance of a conductoro The induced electromotive force of

dissimilar metals in an electrical circuito The color of an object

The choice of thermometric property/substance for temperature measurements depends on the range of temperature to be measured and the application.

Examples:

Mercury is often used in meteorological thermometers, but alcohol is preferred in some cases because it has a much lower freezing point than mercury.

For measuring very high temperature, an optical pyrometer (in which the thermometric property employed is the color of an object) is used

Important characteristics of a thermometer include

• Sensitivity• Accuracy• Reproducibility• Speed

Temperature scales

A number of temperature scales have been used since early 18th century.

They are:

o The Fahrenheit scaleo The Celsius scaleo The Rankine scaleo The Kelvin scale

The Fahrenheit scale(After Gabriel D. Fahrenheit, 1686-1736)

This scale was set up using the following two fixed point temperatures:

Freezing point of water 32oFBoiling point of water 212oF

Initially, Fahrenheit used the body temperature (96oF) as the upper fixed point. Later, the upper fixed point was changed to the boiling point of water. This change gives body temperature as 98.6oF.

The Celsius scale(After Anders Celsius, 1701-1744)

This scale was set up also using the freezing point and the boiling point of water:

Freezing point of water 0oCBoiling point of water 100oC

The original scale of Anders Celsius had larger numbers corresponding to lower temperatures, but it was soon reversed. The Celsius scale was also referred to as centigrade scale earlier because there are 100 degrees between the two fixed points.

The Kelvin scale(After Lord Kelvin, William Thomson, 1824-1907)

This scale is based on the theoretically absolute zero of temperature (the state of minimum thermal energy) and uses degrees equal in size to the Celsius degree. The standard fixed point adopted is

Triple point of water 273.16K

The triple point of water is a state at which liquid water, steam (gaseous water) and ice (solid water) coexist in equilibrium. It occurs a single combination of temperature (273.16K or 0.1oC) and pressure (4.58 mm of mercury).

The Rankine scale(After William John Macquorn Rankine, 1820-1872)

This scale is also based on the theoretically absolute zero of temperature but uses degrees equal in size to the Fahrenheit degree. Hence, the freezing of water is 491.67oR (273.15 x 9/5)

The Rankine scale has been frequently used in engineering and industry.

Fo Co K Ro

Boiling point of water

212 100 373.15 672.67

Triple point of water

32.02 0.01 273.16 491.69

Freezing point of water

32 0 273.15 491.67

Absolute zero -459.67 -273.15 0 0

Relations among Fahrenheit, Celsius, Kelvin and Rankine temperatures

Liquid-in-glass thermometers

This is a common type of thermometers in everyday use. The bulb is usually filled with mercury or alcohol that expands into a capillary tube when heated. In this case the thermometric property is the change in volume of the thermometric liquid. Any temperature change can be defined as being proportional to the change in length of the liquid column.

Bulb filled with thermometric liquid

Capillary tube

Bimetallic strip thermometer

A bimetallic strip is made of two different metal strips welded together. It bends as the temperature changes because the two metals expand by different amounts when heated. It is usually used in a thermostat to break or make an electrical circuit for regulating the temperature of an enclosed space.

Lower temperature Higher temperature

Thermocouple

It makes use of the fact that junctions between dissimilar metals or alloys in an electrical circuit give rise to an electromotive force or voltage if they are at different temperature.

Melting ice

To potentiometer

Copper wire

Copper wire

Wire A

Wire B

Reference junctions

Test junction

The test junction functions as the temperature probe, which is often embedded in the material whose temperature is to be measured. Since the test junction is small an has a small mass, it can follow temperature changes rapidly and come to equilibrium quickly. The thermocouple is widely used in research and engineering laboratories.

Thermocouple (cont.)

The electrical resistance of all metals increases with temperature. The resistance of platinum is more uniform the most metals and can be used to measure temperatures accurately in the range 260oC – 600oC. The metal of the resistance thermometer can be in the form of a thin wire coil enclosed in a thin-wall silver tube for protection or just a thin wire wound around a mica frame. The resistance of the metal wire can be found by passing a current through it and measuring the resulting voltage, which can then be converted to temperature by means of a standard formula.

At lower temperatures, the resistance of an ordinary carbon resistor can be used.

Resistance thermometers

An optical pyrometer consists essentially of a telescope, a read glass filter and a small electric lamp bulb connected in series with a variable resistor, a ammeter and a battery (or power supply). The lamp bulb is incorporated into the telescope at its focus so that the filament of the lamp appears superimposed on the image of the hot object whose temperature is to be measured. The current through the filament is adjusted by varying the resistance until it is neither darker (cooler) than the hot object, nor brighter (hotter).

Since no part of the instrument needs to come into contact with the hot object, the optical pyrometer may be used for very high temperature (above 1300oC) measurements.

The optical pyrometer

Since no part of the instrument needs to come into contact with the hot object, the optical pyrometer may be used for very high temperature (above 1300oC) measurements.

Schematic diagram of an optical pyrometer

A

Hot object

Filter

Telescope

The constant-volume gas thermometer

0

h

Mercury reservoir BA

Scale

Bath or environment to be measured

Pgas

Po

P = Po + gh

The volume of gas in the flask is kept constant by raising or lowering reservoir B to keep the mercury level in column A constant (at the scale level 0).

Pressure vs temperature for constant volume

The diagram below show a typical graph of P vs T taken with a constant-volume gas thermometer. The two dots represent the calibration points at freezing and boiling points of water.

0oC 100oCT(oC)

P

Features of constant-volume thermometer

The constant-volume thermometer is outstanding in its sensitivity, accuracy and reproducibility. However, It is relatively large, bulky and slow in coming to thermal equilibrium. Hence, it is mainly used to measure certain fixed points by which other thermometers can be calibrated.

Experiments show that the readings of constant-volume gas thermometers employing different gases agree reasonably well as long as the gas pressure is low and the temperature is well above the point at which the gas liquefies. The agreement improves as the pressure reduced.

Absolute zero

When the P-T curve of a constant-volume gas thermometer is extrapolated toward negative temperature, it intercepts the T-axis at -237.15oC. This temperature (which corresponds to zero pressure) is the absolute zero temperature mentioned earlier, and has defies all attempts to reach it experimentally. This intercept of the P-T curve does not depend on the type of gas

used.

0oC 100oCT(oC)

P

-273.15oC

gas A

gas B

gas C

Features of constant-volume thermometer

The constant-volume thermometer is outstanding in its sensitivity, accuracy and reproducibility. However, It is relatively large, bulky and slow in coming to thermal equilibrium. Hence, it is mainly used to measure certain fixed points by which other thermometers can be calibrated.

Experiments show that the readings of constant-volume gas thermometers employing different gases agree reasonably well as long as the gas pressure is low and the temperature is well above the point at which the gas liquefies. The agreement improves as the pressure reduced.

Thermal expansion of solids and liquids

Most (but not all) solids and liquids expand when heated. Thermal expansion is a consequence of the average change of separation between the constituent atoms in an object.

One of the exceptions is CaCO3. It expands along one direction and contract along another as its temperature is increased.

Unusual behavior of water

Liquids generally increase in volume with increasing temperature. Water is an exception to this rule in the temperature range 0 – 4oC.

0 2 4 6 8 10

1.0004

1.0003

1.0002

1.0001

1.0000

Temperature oC

Vol

ume

of 1

g of

wat

er

Linear expansion

If thermal expansion is sufficiently small relative to the object’s initial dimensions, the fractional change in any dimension is, to a good approximation, linearly proportional to the temperature change, i.e.

LL

T ,

or L = ·L·T ,

where, the proportional constant is called the average coefficient of linear expansion.

Average linear expansion coefficients of some solids(near room temperature)

Quartz (fused) 0.4 x 10-6 (oC)-1

Invar (Ni-Fe alloy) 0.9 x 10-6 (oC)-1

Glass (Pyrex) 3.2 x 10-6 (oC)-1

Glass (Ordinary) 9 x 10-6 (oC)-1

Steel 11 x 10-6 (oC)-1

Concrete 12 x 10-6 (oC)-1

Copper 17 x 10-6 (oC)-1

Brass 19 x 10-6 (oC)-1

Aluminum 24 x 10-6 (oC)-1

Lead 29 x 10-6 (oC)-1

The length of a bimetallic bar made of a brass strip and a steel strip is 30 cm. Both strips have the same thickness 0.5 mm. The bimetallic bar is straight at 25oC. What is the angle of bending at 45oC?

Example

r2

r1

Brass

Steel

r2 = L (1 + 2 T)

r1 = L (1 + 1 T)

L (2 - 1) Tr2 - r1 =

Let L = length of bimetallic bar at 25oC

1 = average linear expansion coefficient of steel

2 = average linear expansion coefficient of brass

= L (2 - 1) T

r2 - r1=

30x (19x10-6 – 11x10-6) x20

0.05= 0.096 rad = 5.5o

Volume expansion

If thermal expansion is sufficiently small relative to the object’s initial dimensions, the fractional change in volume is, to a good approximation, also linearly proportional to the temperature change, i.e.

VV

T ,

or V = ·V·T ,

where, the proportional constant is called the average coefficient of volume expansion.

Average volume expansion coefficients of some liquids(near room temperature)

Alcohol 1.12 x 10-4 (oC)-1

Benzene 1.24 x 10-4 (oC)-1

Acetone 1.5 x 10-4 (oC)-1

Mercury 1.82 x 10-4 (oC)-1

Water (20oC) 2 x 10-4 (oC)-1

Glycerin 4.85 x 10-4 (oC)-1

Water (50oC) 6 x 10-4 (oC)-1

Turpentine 9.0 x 10-4 (oC)-1

Gasoline 9.6 x 10-4 (oC)-1

Relation between and

There is a simple relation between the average coefficient of linear expansion and that of volume expansion , which can be derived as follows:

Consider a solid having the dimensions x, y and z at temperature T. Its volume at T is hence V = x·y·z. At temperature T + T, its volume will be expanded to V + V, where

V = ·V·T

V can also be expressed in terms of x, y, z, and T:

V = (x + x)·(y + y)·(y + y) - x·y·z = (x + ·x·T )·(y + ·y·T )·(y + ·y·T ) - x·y·z = x·y·z·(1+ ·T )3 - x·y·z = V·[1 + 3·(·T) + 3·(·T)2 + (·T)3] - V = V·[3·(·T) + 3·(·T)2 + (·T)3]

If ·T << 1, which is usually the case for T < ~100o, the 2nd and 3rd order terms of (·T) can be neglected. We have:

V 3··V·T

Therefore 3·

Properties of an ideal gas

The equation that interrelates the pressure, the temperature and the volume of a gas is called the equation of state. In general, the equation of state a gas is very complicated. If the pressure of the gas is maintained at a very low pressure (or low density), the equation of state is quite simple. Such a low-density gas is commonly referred to ideal gas.

The ideal gas law

PV = nRT

The equation of state of an ideal gas is:

whereP = the pressureV = the volumeT = the absolute temperaturen = the number of moles of gas in V = mass/molar massR = a constant called the universal gas constant

Units of R

In SI units, where P is expressed in pascals (1 Pa = 1 N/m2) and V in cubic meters, the product PV has the units of newton·meters (or Joules) and R has value

R = 8.315 J/(mol·K)

If P is expressed in atmospheres and V in liters, then R has the value:

R = 0.08214 L·atm/(mol·K)

From the ideal gas law, it can be noted that when an ideal gas is kept at constant volume,

P T

This property is employed in the constant-volume gas thermometer for temperature measurement.

When the temperature is kept constant,

P 1/V

This is also known as the Boyle’s law.

When the pressure of the law is kept constant,

V T

This is the Charles and Gay-Lussac law.

Boltzmann’s constant

The ideal gas law if often expressed in terms of the total number of molecules N and Boltzmann’s constant kB:

PV = N kB T

where

kB = R / Avogadro’s mumber

= 8.315 / (6.022 x 10+23) J/K

= 1.381 x 10-23 J/K

What is the average volume expansion coefficient of an ideal gas at constant pressure and 0oC?

Example

V = ·V·T

V

V T

1· =

V1 nR

P· =

T1

= 1

273.15 K

= 3.66 x 10-3 K-1