1. 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 2. Temperature scales T C :0°C - freezing of water, 100°C - boiling of water T F = (9/5) T C +32 T C = (5/9) (T F - 32) T k = T C +273.15

2. The temperature of an ideal monatomic gas is a measure related to the average kinetic energy of its atoms as they move. 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

3. At what temperature do they read the same number? That is, at what temperature is T(˚C) = T(˚F)? Question 1. 40 2. 20 3. 0 4.-20 5.-40 Two thermometers are in thermal equilibrium with each other. One reads in ˚C and one reads in ˚F.

4. The Gay-Lussaec law P/T=const P 1 /T 1 = P 2 /T 2 V 2 > V 1 T(K) P V1V1 2a. The absolute (Kelvin) scale and gas thermometer For an ideal gas at V=const: T( ° C) P -273.15°C T( K ) P Definition: T triple = 273.16 K = 0.01 ºC 0°C 0273.15

5. 3. Thermal expansion T 0, L 0 ΔL = α L 0 ΔT + ΔL T = T 0 + ΔT, L = L 0 L - L 0 = α L 0 ΔT L = L 0 (1 + α ΔT) ΔV = β V 0 ΔT V = V 0 (1 + β ΔT) V=L 3 L L V = L 3 =[L 0 (1 + α ΔT)] 3 = L 0 3 (1 + α ΔT) 3 ~ ~ L 0 3 (1 + 3α ΔT) β = 3α ΔA = 2 α A 0 ΔT A= A 0 (1 + 2 α ΔT) A=L 2 L L

6. Example 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 1: An aluminum flagpole is 33m high. By how mach does its length increase as the temperature increases by 15 °C? L 0 = 33 m ΔT = 15 ° C α = 25x10 -6 (C ° ) -1 ΔL = α L 0 ΔT ΔL - ? ΔL = [25x10 -6 (C ° ) -1 ]x (33 m) x (15 ° C) =1.2x10 -2 m

7. The increase in length of the measuring tape upon heating to 40 ˚C is ___ mm. (For steel,  = 1.2 x 10  5 /˚C) Question 1. 0.8 2. 1.6 3. 2.4 4. 3.2 A steel measuring tape is 10.000 m long at 20 ˚C.