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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 � .)
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
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