Physics 121 April 15 2008 Temperature Heat and the Ideal Gas Law http www brickinfo org BIA technotes t18 htm Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 121 April 15 2008 Course information Topics to be discussed today Temperature review The universal gas law Frank L H Wolfs Department of Physics and Astronomy University of Rochester Physics 121 April 15 2008 Homework set 9 is now available and is due on Saturday morning April 19 at 8 30 am Midterm Exam 3 will take place on Tuesday April 22 between 8 00 am and 9 30 am in Hubbell The material to be covered is the material contained in Chapters 10 11 12 and 14 There will be extra office hours on Sunday and Monday Details will be announced via email Frank L H Wolfs Department of Physics and Astronomy University of Rochester Homework set 9 All about simple harmonic motion In all cases a 2x Frank L H Wolfs Department of Physics and Astronomy University of Rochester Temperature a quick review Measuring temperature In order to measure temperature we must Agree on a standard reference point to which we assign a certain temperature Agree on a unit Agree on a standard thermometer against which all other thermometers can be calibrated The unit of temperature will be the Kelvin K The standard reference point is the triple point of water T 273 16 K http www fluke fr common prod pages pages hart products tpw htm Frank L H Wolfs Department of Physics and Astronomy University of Rochester Temperature a quick review Measuring temperature The standard thermometer is the constant volume gas thermometer The bulb of the thermometer which is filled with gas is put in thermal contact with the system to be studied The reservoir on the right is now adjusted to change the mercury level so that the gas volume remains unchanged The temperature of the body is defined in terms of the pressure p T Cp C p0 gh Frank L H Wolfs Fixed Reservoir h T Department of Physics and Astronomy University of Rochester Temperature a quick review Measuring temperature In general we can thus find the temperature of the body by comparing the measured pressure with the triple point pressure T T3 p p3 273 16 p p3 The method described here depends slightly on the amount and the type of gas in the bulb However this dependence is reduced when we use smaller and smaller amounts of gas Frank L H Wolfs Department of Physics and Astronomy University of Rochester Temperature a quick review Measuring temperature The Kelvin is not frequently used in our daily life More common temperature scales are the Celsius scale 0 is defined as the freezing point of water 100 is defined as the boiling point of water and the Fahrenheit scale 0 was defined as the temperature of a mixture of water ice and ammonium chloride 96 was as the temperature of the blood of Fahrenheit s wife Note initially Fahrenheit divided his scale in 12 segments later he divided each segment in 8 smaller segments Frank L H Wolfs Department of Physics and Astronomy University of Rochester Thermodynamic variables Pressure Pressure is an important thermodynamic variable Pressure is defined as the force per unit area The SI unit is pressure is the Pascal 1 Pa 1 N m2 Another common unit is the atm atmospheric pressure which is the pressure exerted by the atmosphere on us 1 atm 1 013 x 105 N m2 A pressure of 1 atm will push a mercury column up by 76 cm Frank L H Wolfs Department of Physics and Astronomy University of Rochester Thermodynamic variables Pressure Many devices that measure pressure actually measure the pressure difference between the pressure of interest and the atmospheric pressure Atmospheric pressure changes with altitude The higher you go the less air is pressing on your head Airplanes use the atmospheric pressure to measure altitude But keep into consideration that the atmospheric pressure at a fixed location and altitude is not constant Frank L H Wolfs Department of Physics and Astronomy University of Rochester Thermodynamic variables Pressure Frank L H Wolfs Department of Physics and Astronomy University of Rochester Thermal expansion Linear expansion When the temperature of a material increases its length will increase L L T The coefficient is the coefficient of linear expansion Typical values are 0 5 x 10 6 K 1 and 10 x 10 6 K 1 at room temperature Note a solid will expand in every direction Frank L H Wolfs Department of Physics and Astronomy University of Rochester Thermal expansion Linear expansion In everything we design we need to consider the effects of thermal expansion Draw bridges must be able to open in summer and winter Airplanes expand in flight due to friction with the air The width of the Concorde increases by a few cm during its flight Frank L H Wolfs Department of Physics and Astronomy University of Rochester Thermal expansion Volume expansion When we deal with liquids we usually talk about volume expansion V V T The coefficient is the volume expansion coefficient The coefficient of volume expansion is related to the coefficient of linear expansion Frank L H Wolfs Department of Physics and Astronomy University of Rochester Relation between volume and linear expansion Consider a volume V whose temperature is increased by T V L L W W H H LWH WH L LH W WL H L H W V V 3 T L H W We see that 3 Frank L H Wolfs Department of Physics and Astronomy University of Rochester Volume expansion The water anomaly Water has a very different thermal behavior from other liquids It expands when it is cooled below 4 C Its expansion continues even below the freezing point frozen pipes This is why ice cubes float The anomalous behavior of water effects the way bodies of water freeze The body of water will cool down until it has a uniform temperature of 4 C Ice will form on top life continues below Frank L H Wolfs Department of Physics and Astronomy University of Rochester Volume expansion A microscopic view The atoms in a solid are held together in a three dimensional periodic lattice by springlike interaction forces The potential energy for a pair of neighboring atoms depends on their separation r and has a minimum at r r0 The distance r0 is the lattice spacing of a solid when the temperature approaches zero The potential energy curve rises more steeply when the atoms are pushed together r r0 than when they are pulled apart r r0 The average separation distance at a temperature above the absolute zero will therefore be larger than r0 A solid with a symmetric potential energy curve