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CLB 10102 PHYSICS CHAPTER 10 Thermal Expansion CLB 10102 Physics CHAPTER 10 Thermal Expansion 10.1 Expansion and Contraction • As the average energy of particles increases, the spaces between the particles increases. They expand (increase their volume) as the temperature increases. • As the average energy of particles decreases, the spaces between the particles decreases. They contract (decrease their volume) as the temperature decreases. • Pure substances are matter that are made up of only one kind of particle, which can be a solid liquid or a gas. • These phases, or states have very specific properties in relation to the particle model. CLB 10102 Physics CHAPTER 10 Thermal Expansion Expansion in Solids • Most solids expand when heated and contract when cooled. • They expand or contract in all three dimensions – length, width and thickness. • When a solid is heated, the expansion is due to the increased length of the vibrations of the atoms and molecules. • This results in the solid expanding in all directions – volume increased, weight density decreased. CLB 10102 Physics Expansion and Contraction in Gases CHAPTER 10 Thermal Expansion CLB 10102 Physics CHAPTER 10 Thermal Expansion • When the particles in a gas are heated, their average energy increases and they need more room, so they expand. • When the particles in a gas are cooled, the volume decreases, or contracts, because the particles need less room. • Under extremely high temperature conditions (like the temperatures inside the Sun, particles can be split into what makes them up (electrons and ions). This creates a fourth state of matter called plasma. CLB 10102 Physics Expansion and Contraction in Liquids CHAPTER 10 Thermal Expansion CLB 10102 Physics CHAPTER 10 Thermal Expansion • When the particles in a liquid are heated, their average energy increases and they need more room, so they expand. • When the particles in a liquid are cooled, the volume decreases, or contracts, because the particles need less room. • This is demonstrated by the liquid used in a thermometer. • As the liquid expands and contracts, it moves up and down the inside tubing the thermometer. CLB 10102 Physics CHAPTER 10 Thermal Expansion 10.2 Coefficient of Linear Expansion • The linear expansion of a heated solid or liquid can be measured by a quantity α, the coefficient of linear expansion. • This coefficient is defined in such a way that it measures the percentage change in the length per degree temperature change. • The change in length, per unit original length per 1oC change in temperature, is called the coefficient of linear expansion. L LoT ∆L = change in length α = coefficient of linear expansion Lo = original length ∆T = change in temperature CLB 10102 Physics CHAPTER 10 Thermal Expansion • Expansions in surface area and volume are negligible. • A varies slightly over a range of temperatures, but the variation is negligibly small. • The amount that a solid expands depends on the following: Material. Different materials expand at different rates. Steel expands at a rate less than that of brass. Length of the solid. The longer the solid, the larger is the expansion. Amount of change in temperature. The greater the change in temperature, the greater is expansion. CLB 10102 Physics CHAPTER 10 Thermal Expansion Example: A steel bridge is built in several segments, each 20 m long. The gap between segments is 4 cm at 18 °C. What is the maximum temperature that the bridge can manage before buckling? [Coefficient of thermal expansion of steel, αsteel is 12 x 10-6 K-1] L LoT 0.04 m = (20 m)(12 x 10-6 K-1)∆T ∆T = 0.04 m (20 m)(12 x 10-6 K-1) = 166.67 K Tf = ∆T + To = 166.67 K + (18 + 273.15 K) = 457.82 K @ 184.67oC CLB 10102 Physics CHAPTER 10 Thermal Expansion 10.3 Coefficient of Superficial Expansion • The change in surface area per unit original area per 1oC change in temperature is called the coefficient of superficial expansions. A 2AoT • Expansion in volume is negligible. , Ao = original area CLB 10102 Physics CHAPTER 10 Thermal Expansion 10.4 Coefficient of Cubic Expansion • The change in volume per unit original volume per 1oC change in temperature is called coefficient of cubical expansion. V 3VoT , Vo = original volume Coefficients of Thermal Expansion for Selected Materials Material aluminium barium ferrite Linear α (10−6 K−1) Material Linear α (10−6 K−1) 23.1 platinum 8.8 10 plutonium 54 brass 20.3 silicon 4.68 carbon, diamond 1.18 silver 18.9 carbon, graphite || 6.5 solder, lead-tin 25 carbon, graphite ┴ 0.5 steel, stainless 17.3 chromium 4.9 steel, structural 12 tin 22 concrete 8 ~ 12 copper 16.5 titanium 8.5 germanium 6.1 tungsten 4.5 glass 8.5 uranium 13.9 gold 14.2 water, ice (0 °C) iron 11.8 zinc 30.2 lead 28.9 nickel 13.3 51 Coefficients of Thermal Expansion for Selected Materials Material Volume β (10−6 K−1) alcohol, ethyl 1120 gasoline 950 jet fuel, kerosene 990 mercury 181 water, liquid (1 °C) -50 water, liquid (4 °C) 0 water, liquid (10 °C) 88 water, liquid (20 °C) 207 water, liquid (30 °C) 303 water, liquid (40 °C) 385 water, liquid (50 °C) 457 water, liquid (60 °C) 522 CLB 10102 Physics CHAPTER 10 Thermal Expansion 10.5 Practical Application of Thermal Expansion Clinical Thermometer • Another thermometer that you are probably familiar with is the clinical thermometer. • It also uses expansion and contraction of a liquid to measure temperature. • But it must be sensitive to a very small changes in temperature, and able to measure temperatures only within a few degrees of normal body temperatures (37ºC). • As the liquid is warmed by the patient's body heat, it expands past the constriction to show the patient's temperature. • After the thermometer has been removed from the patient's mouth, the liquid cools and contracts. • But the liquid cannot move past the constriction; it must be forced back by shaking the thermometer downward. CLB 10102 Physics CHAPTER 10 Thermal Expansion Thermostat • A thermostat can be used to measure temperature in an appliance, such as a furnace, or in a room. • It can also switch appliances on or off at a preset temperature. • Thermostats use the expansion and contraction of solids to measure temperature. • They contain a strip of two metals (called a bimetallic strip). When heated or cooled, the two metals expand or contract by different amounts, causing the strip to bend. • The amount of bending depends on the temperature. It provides a measure of the temperature. CLB 10102 Physics CHAPTER 10 Thermal Expansion Outdoor Thermometer • One thermometer that you are probably familiar with is the outdoor thermometer. • It uses the expansion and contraction of a liquid to measure temperature. • The liquid in the bulb (usually ethyl alcohol with colouring added) expands when it is warmed and is forced up the narrow bore on its temperature. • The more the liquid cools. It contracts, dropping lower in the bore.