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Thermodynamics I. Temperature 1. Thermal equilibrium. Zeroth law of thermodynamics a) We need a thermometer b) Thermal equilibrium c) Zeroth law: If C is in thermal equilibrium with both A and B, then A and B are also in thermal equilibrium with each other d) Temperature Two systems are in thermal equilibrium if and only if they have the same temperature 1

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Question: Two thermometers are in thermal equilibrium with each other. One reads in ˚C and one reads in ˚F. At what temperature do they read the same number? That is, at what temperature is T C = T F ? 2. Temperature scales T C :0°C - freezing of water, 100°C - boiling of water 2

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3. Thermal expansion T 0, L 0 ΔL = α L 0 ΔT + ΔL T = T 0 + ΔT, L = L 0 L = L 0 (1 + α ΔT) ΔV = β V 0 ΔT V = V 0 (1 + β ΔT) V=L 3 L L β = 3α ΔA = 2 α A 0 ΔT A = A 0 (1 + 2 α ΔT) A=L 2 L L 3 α – linear coefficient of thermal expansion β – volumetric coefficient of thermal expansion

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Question 2: A donut shaped piece of metal is cooled and its temperature decreases. What happened with inner and outer radii after cooling? Both radii decrease! Example: An aluminum flagpole is 30 m high. By how much does its length increase as the temperature increases by 20°C? For aluminum the linear coefficient of thermal expansion is 25x10 6 (1/˚C). ΔL = α L 0 ΔT ΔL - ? 4 Question 1: A steel measuring tape is 10.000 m long at 20.0 ˚C. The increase in length of the measuring tape upon heating to 40.0 ˚C is ___ mm. For steel, = 1.2 x 10 5 (1/˚C) A) 0.8 B) 1.6 C) 2.4 D) 3.2

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1. Isotherms (Boyle’s law): T=const II. Ideal gases Equation of state n = m/μ PV=const P 1 V 1 = P 2 V 2 T1T1 T 2 > T 1 V P n - number of moles m - total mass of gas μ - molar (atomic) mass (“weight”) 5

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2. Isobars (Charles’s law): P=const V/T=const V 1 /T 1 = V 2 /T 2 P1P1 P 2 > P 1 T(K) V 3. Isochors (Gay-Lussaec ): V=const P/T=const P 1 /T 1 = P 2 /T 2 V1V1 V 2 > V 1 T(K) P T(C) V -273.15°C T( ° C) P -273.15°C0°C 6

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Example 1: The temperature of an amount of an ideal gas has been increased twice, while the volume has been increased four times. What happened with the pressure? T 2 = 2T 1 V 2 = 4V 1 P 2 /P 1 - ? Example 2: What is the volume of 1 mole of an ideal gas at “standard temperature and pressure”? n = 1 mol T = 273 K (0° C) P = 1 atm = 1.013x10 5 Pa V - ? 7

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In this animation, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure. These room-temperature atoms have a certain, average speed (slowed down here two trillion fold). Heating a body, such as a segment of protein alpha helix, tends to cause its atoms to vibrate more, and to cause it to expand or change phase. http://en.wikipedia.org/wiki/Temperature The temperature of an ideal monatomic gas is a measure related to the average kinetic energy of its atoms as they move. 8

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