Chapter 16: Temperature and Heat

1. Chapter 16: Temperature and Heat • Now, we move to a new area and take up the study of Thermodynamics (skip Chap. 15) • 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. 15, sections 1-3): - Density (or mass density)

2. Specific Gravity • Pressure • Consider a swimming pool of surface area A and depth h which is filled with water (total mass m) A FBD Ft=PtA h h mg There is a pressure Pt on top of the water due to the column of air above Fb=PbA

3. Pt is equal to the atmospheric pressure = 1.01x105 Pa (at sea level) = 1 atmosphere  1 bar (1 bar 105 Pa) • To determine pressure at the bottom of the pool, apply Newton’s 2nd Law • The density of the water and the volume of the water are

4. °F °C • Therefore, the change in pressure from the bottom to top is - Temperature K Boiling point of water Freezing point of water (at sea level and 1 atmosphere) 212 100 372.15 32 0 273.15 -459.7 -273.15 0 • The Kelvin (K) scale is an absolute temperature scale – 0 K is absolute minimum temperature (no negative values)

5. 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 0th-2nd Laws) • However, experiments have been performed in which a gas has been cooled to 100 nK. • 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 (sect. 17-2)

6. Effect of Temperature Changes on Liquids and Solids • Consider a thin rod of length L0 at initial temperature T0. • If it is heated to a warmer temperature Tf, its length will increase to a new length Lf  Linear ThermalExpansion of a Solid Lo  = coefficient of linear expansion (solids only), depends on the material (see Table 16-1), has units of (C°)-1 or K-1 Tf>T0 Lf Lf Tf<T0

7. Can also be applied to a hole in a material. Consider a thin board with a circular hole of diameter D0 which is heated from T0 to Tf • 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 V0 and T0 T0 Tf

8. Tf>T0 T0,V0 =coefficient of volume expansion, depends on substance (see Table 16-1), units of (C°)-1 or K-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?

9. Solution: Given: L0=76 m, r0=9.5x10-3 m, T0=24°C, Tf=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 expands. The difference is the volume needed for the expansion tank. From Table 16-1 get coefficients of volume expansion What is the volume of the pipe interior?

10. For volume expansion use Where the change in temperature