11 22 2010 Mid term results Thermal physics 1 11 22 2010 Zeroth law of thermodynamics If objects A and B are separately in thermal equilibrium with a third object C then A and B are in thermal equilibrium with each other Thermometers in celsius scale The celsius temperature scale is defined in terms of the freezing point and the boiling point of water 2 11 22 2010 Other scales for temperature Kelvin scale used the absolute zero and the triple point of water to be the references and the size of a degree is made the same as the celsius scale Tc T 273 15 1 Kelvin SI unit of temperature is 1 273 16 of the temperature of the triple point of water Temperature in Kelvin 3 11 22 2010 Thermometers changing scales Tc T 273 15 9 TF Tc 32 5 5 Tc TF 32 9 Temperature question time After this phy231 lecture a student puts one hand on a metal table and one hand on the cushioned seat What does she conclude about the relative temperatures at which the table and seat are a Temperature of seat temperature of table b Temperature of seat temperature of table c Temperature of seat temperature of table 4 11 22 2010 Temperature question time A child is measuring a temperature of 420C in a European thermometer What should you do a Send the child to the playground to play b Put the child in a warm bath so her temperature can increase c Immediately give the child tylenol to reduce the fever Thermal linear expansion in solids The length increase of a solid with initial length L0 is proportional to the change in temperature L L0 T Coefficient of linear expansion 5 11 22 2010 Linear expansion question time A steel railroad track has a length of 30 000 m when the temperature if 0 00 0C What is its length in a hot day when the temperature is 40 0 0C If the track is nailed down and cannot expand what would the stress be due to the temperature change Linear expansion thermostats 6 11 22 2010 Thermal expansion in solids The area increase of a solid with initial area A0 is proportional to the change in temperature A A0 T Coefficient of area expansion Thermal expansion in solids V V T The volume increase of a solid with initial volume V0 is 0 proportional to the change in temperature Coefficient of volume expansion If expansion is the same in all directions 2 3 7 11 22 2010 Volume expansion question time Estimate the fractional change in the volume of the Earth s oceans due to an average temperature increase of 1 0C Use the fact that the depth of the ocean is 4 00 x 103 m to estimate the change in depth Note that 2 07x104 0C 1 Unusual behaviour of water Why to ponds freeze from the top Why can pipes in your apartment break when you go home for Xmas break 8 11 22 2010 Ideal gas macroscopic description The pressure P the volume V the temperature T and the amount of gas n are related to each other through the equation of state Ideal gas Collection of atoms or molecules considered point like that move randomly and exert no long range forces on each other Avogardo s number number of particle per mole N A 6 02 10 23 Ideal gas equation of state The ideal gas law is PV nRT Universal gas constant R 8 31 J mol K 9 11 22 2010 Ideal gas question time An ideal gas at 20 0 0C and pressure 1 50x105 Pa is in a container of volume 1 00 L a Determine the number of moles of gas in the container b The gas pushes against the piston expanding to twice its original volume while the pressure falls to atmospheric pressure Find the final temperature Ideal gas question time A beachcomber finds a corked bottle containing a message The air in the bottle is at atmospheric pressure and temperature 30 0 0C The cork has a cross sectional area of 2 30 cm2 The beachcomber places the bottle over the fire assuming the increase pressure will push out the cork At the temperature of 99 0C the cork is ejected from the bottle a What was the pressure in the bottle just before the cork was ejected b What force of friction held the cork in place 10 11 22 2010 Ideal gas kinetic theory Assumptions 1 The number of molecules in a gas is large and the average separation between them is large compared with their dimension 2 The molecules obey Newton s laws of motion but as a whole they move randomly 3 The molecules interact only via short range forces during elastic collisions 4 The molecules make elastic collisions with the walls 5 All molecules in the gas are identical Ideal gas kinetic theory The pressure is proportional to the number of molecules per unit volume and to the average translational kinetic energy of a molecule 2 N 1 P mv 2 3 V 2 11 11 22 2010 Molecular interpretation of temperature Temperature of a gas is a direct measure of the average molecular kinetic energy of the gas T 2 1 2 mv 3k B 2 where kB R N A The total translational kinetic energy of a system of molecules is proportional to the absolute temperature of the system 1 3 3 KEtot N mv 2 Nk BT nRT 2 2 2 Internal energy The internal energy for a monoatomic gas is U 3 nRT 2 The root mean square speed is vrms v2 3k BT 3RT m M 12 11 22 2010 Root mean square speed Kinetic theory question time A cylinder contains 2 00 mol of helium gas at 20 0 0C Assume the helium behaves like an ideal gas a Find the total internal energy of the system b What is the average kinetic energy per molecule c How much energy would you have to add to the system to double the rms speed 13
View Full Document
Unlocking...