The Phases of Matter

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Thermodynamics

SOME DEFINITIONS:

• THERMO – related to heat

• DYNAMICS – the study of motion

• SYSTEM – an object or set of objects

• ENVIRONMENT – the rest of the universe

• MICROSCOPIC – at an atomic or molecular level

• MACROSCOPIC – at a level detectable by our senses

THERMODYNAMICS

¾ is the study of the relationship between heat and motion.

¾ is a macroscopic description of the properties of a system using state variables (e.g. volume, temperature, pressure) Atoms are in constant motion, which increases with temperature.

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The Phases of Matter

+ - + - + - - + - + - + - + - + - - - + - + - + + - - - + - + - + + - - - + - + - + + - - - + - + - + + - - - + - + + + - + - + - + - + + -

- - + - + - + - - - + - + - + + - + - + - + - + -

Solid Liquid Gas or Vapor Plasma

Increasing Temperature

Solids and liquids composed of atoms joined together at distances of about 10^-10 m by attractive electrical forces. In gases, vapors

and plasmas, the atoms, molecules or ions are in random motion.

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Temperature

Temperature

• is a measure of how hot or cold an object is.

• is measured by a thermometer.

Thermometers are based on physical properties of objects that change with temperature, for example:

¾ volume of a liquid

¾ length of a solid

¾ pressure of a gas

¾ electrical resistance of a solid

¾ electrical potential difference between two solids.

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Common Temperature Scales

Fahrenheit:

• Based on the ability of farm animals to survive for extended periods without attention.

(0ÈF is the coldest and 100ÈF is the hottest).

Celsius or Centigrade:

• Based on the physical properties of water on the

earth’s surface at sea level (0ÈC is the freezing point and 100ÈC is the boiling point).

T(ÈC) = (5/9)[T(ÈF) – 32]

T (ÈF) = (9/5)T(ÈC) + 32

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Zero’th Law of Thermodynamics

Our experience tells us that objects placed in contact will eventually reach the same temperature. We say that they are then in thermal equilibrium. This is the basis for

The Zero’th Law of Thermodynamics:

If two objects A and B are in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other.

Objects or systems in thermal equilibrium have the

same temperature. This is the physical basis for the definition of temperature.

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Questions

• Is it possible for two objects to be in thermal equilibrium if they are not touching each other?

• Can objects that have different

temperatures be in thermal equilibrium

with each other?

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Thermal Expansion

Most materials expand when heated:

¾ The average distance between atoms increases as the temperature is raised.

¾ The increase is proportional to the change in temperature (over a small range

).

Consider an object of length L

_i

at temperature T

_i

¾ If the object is heated or cooled to temperature T_f L_f – L_i = α L_i (T_f – T_i) or ∆L = α L_i ∆T

α = coefficient of linear expansion [ºC^-1] (α is a property of the material)

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Thermal Expansion of Solids and Liquids

For the same temperature change, the thermal

expansion of liquids is much greater than that of solids (> 10 times).

Area Expansion:

∆A = 2α A_i∆T

Volume Expansion

∆V = 3α V_i∆T 12 x 10^-6

Concrete

3.2 x 10^-4 Gasoline

1.8x 10^-4 Mercury

29 x 10^-6 Lead

17 x 10^-6 Copper

9 x 10^-6 Glass

α (ºC ^-1) Material

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Example: Thermal Expansion Problem 17-8.

A concrete highway is built of slabs 12 m long (20 ºC). How wide

should the expansion cracks

between the slabs be (at 20 ºC) to prevent buckling if the range of

temperature is –30 ºC to +50 ºC ?

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Liquid water has an unusual property.

• Water contracts when heated from 0ºC to 4ºC, then expands when

heated from 4 ºC to 100 ºC.

• Just above the freezing point, the coldest (and least dense) water rises to the surface, and

lakes freeze from the surface downward.

• This unusual property permits aquatic life on earth to survive winter!

Density of Water

0.95 0.96 0.97 0.98 0.99 1

0 4 12 20 50 100 Temperature in Celsius

g/(cm**3)

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Thermal Stress

T A E

F

T L

A L F E

T L

L

A L F L E

∆

=

∆

=

∆

=

∆

=

∆

α

α α

0 0

0

1

1 • Heat can stress materials if no allowance is made for thermal expansion:

E = Young’s Modulus Thermal Expansion

Thermal Stress

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Review Questions

• When a cool mercury or alcohol

thermometer is inserted into boiling water, it will initially indicate a lower

temperature before the reading starts to increase. Explain.

• Will a grandfather clock that has been

calibrated at normal room temperature run

fast, slow or the same on a very hot day?

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Absolute (Kelvin) Temperature Scale

The volume occupied by any gas at constant pressure is an increasing linear function of temperature, that always

extrapolates to zero at –273.15 ºC (called absolute zero).

This is called Charles’s Law and is the

basis for the absolute or Kelvin (K)

temperature scale.

T(K) = T(ºC) + 273.15

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Absolute or Kelvin Temperature Scale

¾ The absolute or Kelvin scale is the true physical temperature scale.

¾ T = -273.15 ºC = 0 K is the lowest temperature that can be defined for any physical system.

¾ Absolute zero of temperature (0 K) is a theoretical limit that can never be reached in a physical system.

¾ Experiments on Bose-Einstein Condensation in gases have reached the nano-Kelvin (10^-9 K) range (1998, 2001 Nobel Prizes in physics)!

¾ The degree steps in the Celsius and Kelvin scales are chosen to be the same: ∆T(ºC) = ∆T(K).

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Molecular Model of an Ideal Gas

• The number of molecules is large.

• The average separation between molecules is large compared to their dimensions.

• The molecules obey Newton’s laws of motion and move randomly.

• The molecules collide elastically with each other and with the container walls.

• The forces between molecules are negligible except during collisions.

• All the molecules of the gas are identical.

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Ideal Gas

¾ The relationship between the state variables, pressure P, volume V and temperature T of a system is called its equation of state.

¾ An ideal gas is one whose equation of state is simple:

PV = nRT

n = number of moles (mole = 6.023 x 10²³ molecules) R = universal gas constant = 8.31 J/(mole K)

¾ Most gases near room temperature and

atmospheric pressure behave as ideal gases.

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Avogradro’s Number and Molar Mass

• N

_A

= 6.023 x 10

²³

= Avogadro’s number

• 1 mole is the quantity of any substance that contains Avogadro’s number of atoms or

molecules.

• The gram-molecular-weight M of a substance is the mass of one mole (molar mass) of that

substance:

¾ Helium (He) M = 4 g/mole

¾ Nitrogen (N₂) M = 28 g/mole

¾ Oxygen (O₂) M = 32 g/mole

¾ Methane (CH₄) M = 16 g/mole

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Equation of State of an Ideal Gas

• For a gas containing N atoms or molecules, the number of moles n = N/N_A.

• The ideal gas law:

PV = nRT = (N/N_A)RT = N(R/N_A)T = Nk_BT where

k_B = R/N_A = 1.38 x 10^-23 J/K (Boltzmann’s constant)

• The ideal gas law may be expressed:

PV = Nk_BT (N = number of atoms or molecules) or

PV = nRT (n = number of moles)

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Applying the Ideal Gas Law

)

2 2

1 1

T n

V P T

n V

P =

2 2 2

1 1 1

T V P T

V

P =

or if n

₁

= n

₂

general case closed container

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Example Problem

Problem 17-34.

If 18.75 mol of helium gas is at 10.0ºC and a gauge pressure of 0.350 atm., calculate

a) The volume of the helium gas under these conditions.

b) The temperature if the gas is compressed to precisely half the volume at a gauge

pressure of 1.00 atm.

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Questions

• An ideal gas in a sealed bottle at temperature T occupies a volume V, and exerts a pressure P on the walls of the bottle. What will happen to the pressure if the temperature is doubled?