Temperature & Thermal Expansion

� Temperature

� Zeroth Law of Thermodynamics

� Temperature Measurement

� Thermal Expansion

� Homework

Temperature & Thermal Equilibrium

� Temperature

– Fundamental physical quantity

– Measure of average kinetic energy of molecular motion

� Thermal equilibrium

– Two objects in thermal contact cease to have an exchange of energy

The Zeroth Law of Thermodynamics

If objects A and B are separately in thermal equilibrium with a third object C(the thermometer), the A and B are in thermal equilibrium with each other.

Temperature Measurement

� In principle, any system whose physical properties change with tempera-ture can be used as a thermometer

� Some physical properties commonly used are

– The volume of a liquid

– The length of a solid

– The electrical resistance of a conductor

– The pressure of a gas held at constant volume

– The volume of a gas held at constant pressure

The Glass-Bulb Thermometer

� Common thermometer in everyday use

� Physical property that changes is the volume of a liquid - usually mercuryor alcohol

� Since the cross-sectional area of the capillary tube is constant, the changein volume varies linearly with its length along the tube

Calibrating the Thermometer

� The thermometer can be calibrated by putting it in thermal equilibriumwith environments at known temperatures and marking the end of theliquid column

� Commonly used environments are

– Ice-water mixture in equilibrium at the freezing point of water

– Water-steam mixture in equilibrium at the boiling point of water

� Once the ends of the liquid column have been marked for a couple differ-ent environments, a scale must be defined

The Celsius Scale

� A common temperature scale is the Celsius scale

� On this scale the freezing point is at zero degrees (0 � C) and the boilingpoint is at 100 degrees (100 � C)

The Constant-Volume Gas Thermometer

� The standard thermometer, against which all other thermometers are calibrated

� Measures the pressure of the gas contained in the flask immersed in the bath

� The volume of gas in the flask is kept constant be raising or lowering reservoir B suchthat the mercury level in column A remains constant

� Pressure is determined from the height h of the mercury in the reservoir (P = P �� � + � gh)

Absolute Zero

� Experiments show that the results obtained with the constant-volume gas thermometerare nearly independent of the type of gas used

� If the measurements are performed with the gas in the flask at different starting pressuresat 0� C, different straight-line calibration curves are obtained

� All of these curves extrapolate to zero pressure at the unique temperature of -273.15� C

The Kelvin Scale

� Absolute zero is used as the basis for the Kelvin temperature scale in which -273.15� Cis set as the zero point (0 K)

� The size of a degree on the Kelvin scale is the same as the size of a degree on the Celsiusscale

� The conversion between the Kelvin and Celsius scales is given by T � = T - 273.15

The Fahrenheit Scale

� The most common temperature scale

� The ice point is at 32� F and the steam point is at 212� F

� The relationship between the Fahrenheit scale and the Celsius scale is given by T � =

T � + 32� F

� The relationship between changes in temperature on the two scales is given by � T � =

� T �

Thermal Expansion

� If the temperature of a metal rod of length L � is raised by an amount T,its length is found to increase by an amount

� � �� � �

where � is a constant called the coefficient of linear expansion.

� If the temperature of a solid or liquid whose volume is V � is increased byan amount T, the increase in volume is found to be

� � � � � �where � is the coefficient of volume expansion. (Note that � = 3 � .)

Expansion Coefficients for Some Materials

Example

On a hot day in Las Vegas, an oil trucker loaded 37,000 L of diesel fuel. Heencountered cold weather on the way to Payson, Utah, where the temperaturewas 23.0 K lower than in Las Vegas, and where he delivered his entire load.How many liters did he deliver? The coefficient of volume expansion fordiesel fuel is 9.50 � 10 � � / � C.

The Unusual Behavior of Water

� At temperatures above 4 � C, water behaves like most liquids and contractsas it is cooled

� But, at temperatures below 4 � C it expands as it is cooled

� This is why bodies of water freeze at the surface and why freezing watercan break sealed containers

Homework Set 1 - Due Wed. Jan 7

� Read Sections 16.1 - 16.3

� Answer Questions 16.1, 16.4 & 16.5

� Do Problems 16.1, 16.3, 16.8, 16.13 & 16.14