LECTURE 6 TEMPERATURE & THERMAL EXPANSION Lecture Instructor: Kazumi Tolich Lecture 6 2 ¨ Reading chapter 13-1 to 13-2. ¤ The zeroth law of thermodynamics ¤ Temperature scales ¤ Thermal expansion Heat 3 Heat is defined as the energy transferred between objects because of a temperature difference. ¨ An object does not contain heat. ¨ Objects are in thermal contact if heat flows between them. ¤ The hot object cools off while the cold object warms up. ¨ Objects are in thermal equilibrium when there is no transfer of heat between them. ¨ The study of physical processes involving the transfer of heat is thermodynamics. Thermal equilibrium 4 ¨ Zeroth law of thermodynamics: If two objects are in thermal equilibrium with a third object, then all three of the objects are in thermal equilibrium with each other. ¨ Two objects in thermal contact are in equilibrium when they have the same temperature. Temperature scales 5 ¨ To define a temperature scale we need to define the temperature at two points. ¨ In the Celsius scale, water freezes at 0 ºC and boils at 100 ºC. ¨ In the Fahrenheit scale, water freezes at 32 ºF and boils at 212 ºF. 9 TF = ( 5 Fº Cº)TC + 32 º F 5 TC = ( 9 Cº Fº) (TF − 32 º F) Demo: 1 6 ¨ Liquid crystal sheets ¤ Temperature-sensitive liquid crystal detects changing temperature Constant-volume gas thermometers 7 ¨ By adjusting the level of mercury in the right-hand tube, the level of mercury in the left-hand tube can be set to a fixed reference level. ¨ The gas occupies a constant volume and its pressure is Pgas = Pat + ρgh. Absolute zero and the Kelvin temperature scale 8 ¨ Using a constant-volume gas thermometer, we learn that if we continue to lower the temperature, we eventually reach zero pressure at -273.15ºC, independent of the type of gas. ¨ The Kelvin temperature scale defines 0 K to be exactly at this temperature, absolute zero, and has the same degree size as the Celsius scale. ¨ The conversion between a Celsius temperature and a Kelvin temperature is T = TC + 273.15 Example: 1 9 ¨ A constant-volume gas thermometer has a pressure of P1 = 80.3 kPa at T1 = -10.0 °C and a pressure of P2 = 86.4 kPa at T2 = 10.0 °C. a) At what temperature does the pressure of this system extrapolate to zero? b) What are the pressures of the gas at the freezing and boiling points of water? c) In general terms, how would your answers to parts a) and b) change if a different constant-volume thermometer is used? Thermal expansion 10 ¨ Most substances expand when heated. ¤ An increase in temperature implies an increase in vibrations of atoms. This results in greater spacing among atoms in solids. ¨ Water is one of the exceptions. ¨ Many thermometers measure temperature using the expansion of some material such as mercury or alcohol. Linear, area, and volume expansions 11 ¨ The change in length ΔL is given by ΔL = αL0ΔT ¤ α is coefficient of linear expansion, L0 is the original length, and ΔT is the temperature change. ¨ The change in area ΔA is approximated by ΔA ≈ 2αAΔT ¤ A is the original area. ¨ The change in volume ΔV is ΔV = βVΔT ≈ 3αVΔT ¤ β is coefficient of volume expansion, and V is the original volume. Bimetallic strips 12 ¨ A bimetallic strip consists of two different metals with different coefficients of linear expansion. ¨ Bimetallic strips can be used for thermostats or thermometers. Demo: 2 13 ¨ Bimetallic strip and coil ¤ Demonstration of different thermal expansion in different metals Clicker question: 1 & 2 14 Demo: 3 15 ¨ Ball and hole ¤ Demonstration of thermal area expansion Example: 2 16 ¨ A hole in an aluminum plate has a diameter of d1 = 1.178 cm at T1 = 23.00 °C. a) What is the diameter of the hole, d2, at T2 = 199.0 °C? b) At what temperature, T3, is the diameter of the hole equal to d3 = 1.176 cm? Clicker question: 3 17 Special properties of water 18 ¨ Solid ice is less dense than liquid water. ¤ You can see only ~10% of icebergs above water surface. ¨ The density of water is maximum at 4 °C. ¤ Water shrinks as you heat it from 0 °C to 4 °C. Demo: 4 19 ¨ Density of 4 °C water ¤ Demonstration of why fish can live in lakes during a cold winter ¤ Density of 4 °C water is the highest. .