Chapter 12: Temperature and Heat  Now, we move to a new area and take up the study of Thermodynamics  Thermodynamics deals with the mechanics of a (large) collection of particles (gas, liquid, solid) and how these particles interact (on average) with their environment  First, we need some definitions (see Chap. 11, sections 1-3): - Density (or mass density)

-Specific Gravity -Pressure  Consider a swimming pool of surface area A and depth h which is filled with water (total mass m) h AFBD mg F b =P b A F t =P t A h There is a pressure P t on top of the water due to the column of air above

 P t is equal to the atmospheric pressure = 1.01x10 5 Pa (at sea level) = 1 atmosphere  To determine pressure at the bottom of the pool, apply Newton’s 2 nd Law  The density of the water and the volume of the water are

 Therefore, the change in pressure from the bottom to top is - Temperature °F°C K Boiling point of water Freezing point of water (at sea level and 1 atmosphere)  The Kelvin (K) scale is an absolute temperature scale – 0 K is absolute minimum temperature (no negative values)

 In fact, 0 K can never be reached. This is known as the Third Law of Thermodynamics (Hopefully, we will have time to discuss the 0 th -2 nd Laws)  However, experiments have been performed in which a gas has been cooled to < K.  Converting between scales:  What is temperature? It is a measure of the internal energy of a substance (aggregate random motion of all its atoms and/or molecules)  This energy is proportional to the temperature. For an ideal gas

Effect of Temperature Changes on Liquids and Solids  Consider a thin rod of length L o at initial temperature T o.  If it is heated to a warmer temperature T f, its length will increase to a new length L f  Linear Thermal Expansion of a Solid LoLo LfLf LfLf  = coefficient of linear expansion (solids only), depends on the material (see Table 12.1), has units of (C°) -1 T f >T o T f <T o

 Can also be applied to a hole in a material. Consider a thin board with a circular hole of diameter D o which is heated from T o to T f  Can not be applied to liquids or gases as they have no fixed shape  But for liquids and solids, we have another effect called the Volume Thermal Expansion. It can not be applied to gases as they are compressible.  Consider a substance of volume V o and T o ToTo TfTf

T o,V o T f >T o  =coefficient of volume expansion, depends on substance (see Table 12.1), units of (C°) -1  For solids,  =3  Example: Problem Many hot-water heating systems have a reservoir tank connected directly to the pipeline, so as to allow for expansion when the water becomes hot. The heating system of a house has 76 m of copper pipe whose inside radius is 9.5x10 -3 m. When the water and pipe are heated from 24 to 78 °C, what must be the minimum volume of the tank to hold the overflow of the water?

Solution: Given: L o =76 m, r o =9.5x10- 3 m, T 0 =24°C, T f =78°C Method: Need to know initial volume of pipe interior which is also the initial volume of water. When heated both water and pipe volume expanded. The difference is the volume needed for the expansion tank. From Table 12.1 get coefficients of volume expansion What is the volume of the pipe interior?

For volume expansion use Where the change in temperature