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

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

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

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

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

Kelvin Temperature Scale, 2 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.

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

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

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

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

Thermal Expansion, Example Figure 16.7a: Thermal expansion joints are used to separate sections of roadways on bridges. Without these joints, the surfaces would buckle due to thermal expansion on very hot days or crack due to contraction on very cold days.

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

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

A structural model of atoms in a solid Figure 16.8: A structural model of the atomic configuration in a solid. The atoms (spheres) are imagined to be connected to one another by springs that reflect the elastic nature of the interatomic forces.

Linear Expansion Assume an object has an initial length L That length increases by DL= Lf – Li as the temperature changes by DT=(Tf – Ti) The change in length can be found by DL = a Li DT a is the average coefficient of linear expansion, with the units of (oC)-1

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

Volume Expansion The change in volume is proportional to the original volume and to the change in temperature DV = Vi b DT b is the average coefficient of volume expansion For a solid, b = 3 a This assumes the material is isotropic, the same in all directions For a liquid or gas, b is given in the table

Area Expansion The change in area is proportional to the original area and to the change in temperature DA = Ai g DT g is the average coefficient of area expansion g = 2 a

Thermal Expansion

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

Exercise 59

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. 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.

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

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

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

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

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)

Ideal Gas Law The equation of state for an ideal gas combines and summarizes the other gas laws PV = 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

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

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

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

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

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

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

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