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Constant-Volume Gas Thermometer

The physical property used in this device is the pressure variation with temperature of a fixed-volume gas.

The volume of the gas in the flask is kept constant by raising or lowering the reservoir B to keep the mercury level at A constant

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Constant Volume Gas Thermometer, cont The thermometer is calibrated by using

a ice water bath and a steam water bath The pressures of the mercury under

each situation are recorded The volume is kept constant by adjusting A

The information is plotted

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Constant Volume Gas Thermometer, final To find the

temperature of a substance, the gas flask is placed in thermal contact with the substance

The pressure is found on the graph

The temperature is read from the graph

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Absolute Zero The thermometer

readings are virtually independent of the gas in the flask.

If the lines for various gases are extended, the pressure is always zero when the temperature is –273.15o C

This temperature is called absolute zero

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Kelvin Temperature Scale Absolute zero is used as the basis of

the Kelvin temperature scale. The size of the degree on the Kelvin

scale is the same as the size of the degree on the Celsius scale

To convert: TC = T – 273.15 TC is the temperature in Celsius T is the Kelvin (absolute) temperature

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The Kelvin temperature scale is now based on two new fixed points Adopted in 1954 by the International

Committee on Weights and Measures One point is absolute zero The other point is the triple point of water

This is the single temperature and pressure at which ice, water, and water vapor can coexist in thermal equilibrium.

Kelvin Temperature Scale, 2

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Absolute Temperature Scale, 3 The triple point of water occurs at 0.01o

C and 4.58 mm of mercury This temperature was set to be 273.16K

on the Kelvin temperature scale. The unit of the absolute scale is the kelvin

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Absolute Temperature Scale, 4 The absolute scale is also called the

Kelvin scale Named for William Thomson, Lord Kelvin

The triple point temperature is 273.16 K No degree symbol is used with kelvins

The kelvin is defined as 1/273.16 of the temperature of the triple point of water

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Some Examples of Absolute Temperatures

This figure gives some absolute temperatures at which various physical processes occur

The scale is logarithmic The temperature of

absolute zero has never been achieved.

Experiments only have come close

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Energy at Absolute Zero According to classical physics, the kinetic

energy of the gas molecules would become zero at absolute zero.

The molecular motion would cease Therefore, the molecules would settle out on the

bottom of the container Quantum theory modifies this statement and

indicates that some residual energy would remain at this low temperature. This energy is called the zero-point energy

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Thermal Expansion, Example

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16.3 Thermal Expansion Thermal expansion is the increase in the

size of an object with an increase in its temperature

Thermal expansion is a consequence of the change in the average separation between the atoms in an object

If the expansion is small relative to the original dimensions of the object, the change in any dimension is, to a good approximation, proportional to the first power of the change in temperature

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Thermal Expansion As the washer is heated, all

the dimensions will increase A cavity in a piece of

material expands in the same way as if the cavity were filled with the material

The expansion is exaggerated in this figure

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A structural model of atoms in a solid

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Linear Expansion Assume an object has an initial length L That length increases by L= Lf – Li as

the temperature changes by T=(Tf – Ti) The change in length can be found by

L = Li T is the average coefficient of linear

expansion, with the units of (oC)-1

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Linear Expansion, final Some materials expand along one

dimension, but contract along another as the temperature increases

Since the linear dimensions change, it follows that the surface area and volume also change with a change in temperature

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Volume Expansion The change in volume is proportional to the

original volume and to the change in temperature

V = Vi T is the average coefficient of volume

expansion For a solid, 3

This assumes the material is isotropic, the same in all directions

For a liquid or gas, is given in the table

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Area Expansion The change in area is proportional to

the original area and to the change in temperature

A = Ai T is the average coefficient of area

expansion = 2

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Thermal Expansion

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Application: Bimetallic Strip Each substance has its

own characteristic average coefficient of expansion

This can be used in the device shown, called a bimetallic strip.

It can be used in a thermostat

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Exercise 59

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Water’s Unusual Behavior As the temperature

increases from 0o C to 4o C, water contracts

Its density increases Above 4o C, water expands

with increasing temperature Its density decreases

The maximum density of water (1 000 kg/m3) occurs at 4oC

Matter Macroscopic description Thermodynamics Thermodynamic variables

P (Pressure), V(volume), T (Temperature), N (number of particles), …..

All of these variables are not independent and a function of them is an equation of states of the matter.

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Microscopic description Kinetic theory, Statistical

mechanics, …. Microscopic variables:

Positions and velocities of particles These variables follow the

Newton’s laws of motion. Making an average of the

physical quantities according to the probability theory.

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16.4 Gas: Equation of State It is useful to know how the volume, pressure

and temperature of the gas of mass m are related

The equation that interrelates these quantities is called the equation of state These are generally quite complicated If the gas is maintained at a low pressure, the

equation of state becomes much easier This type of a low density gas is commonly

referred to as an ideal gas

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Ideal Gas – Details A collection of atoms or molecules

Moving randomly Exerting no long-range forces on one

another The sizes are so small that they occupy a

negligible fraction of the volume of their container

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The Mole The amount of gas in a given volume is

conveniently expressed in terms of the number of moles

One mole of any substance is that amount of the substance that contains Avogadro’s number of molecules Avogadro’s number, NA = 6.022 x 1023

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Moles, cont The number of moles can be

determined from the mass of the substance: n = m / M M is the molar mass of the substance

Commonly expressed in g/mole m is the mass of the sample n is the number of moles

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Gas Laws

When a gas is kept at a constant temperature, its pressure is inversely proportional to its volume (Boyle’s Law)

When a gas is kept at a constant pressure, the volume is directly proportional to the temperature (Charles’ Laws)

When the volume of the gas is kept constant, the pressure is directly proportional to the temperature (Guy-Lussac’s Law)

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Ideal Gas Law The equation of state for an ideal gas

combines and summarizes the other gas lawsPV = n R T

This is known as the ideal gas law R is a constant, called the Universal Gas

Constant R = 8.314 J/ mol K = 0.08214 L atm/mol K

From this, you can determine that 1 mole of any gas at atmospheric pressure and at 0o C is 22.4 L

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Ideal Gas Law, cont The ideal gas law is often expressed in

terms of the total number of molecules, N, present in the sample

P V = n R T = (N / NA) R T = N kB T kB= R / NA is Boltzmann’s constant

kB = 1.38 x 10-23 J / K

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16.5 Ludwid Boltzmann 1844 – 1906 Contributions to

Kinetic theory of gases Electromagnetism Thermodynamics

Work in kinetic theory led to the branch of physics called statistical mechanics

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Kinetic Theory of Gases Building a structural model based on the

ideal gas model The structure and the predictions of a

gas made by this structural model Pressure and temperature of an ideal

gas are interpreted in terms of microscopic variables

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Assumptions of the Structural Model

The number of molecules in the gas is large, and the average separation between them is large compared with their dimensions The molecules occupy a negligible volume

within the container This is consistent with the ideal-gas model,

in which we assumed the molecules to be point-like

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Structural Model Assumptions, 2

The molecules obey Newton’s laws of motion, but as a whole their motion is isotropic Meaning of “isotropic”: Any molecule can

move in any direction with any speed

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Structural Model Assumptions, 3 The molecules interact only by short-range

forces during elastic collisions This is consistent with the ideal gas model, in

which the molecules exert no long-range forces on each other

The molecules make elastic collisions with the walls

The gas under consideration is a pure substance All molecules are identical

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Ideal Gas Notes An ideal gas is often pictured as

consisting of single atoms However, the behavior of molecular

gases approximate that of ideal gases quite well Molecular rotations and vibrations have no

effect, on average, on the motions considered