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Unformatted text preview: Lecture 23 Internal Energy, Heat and phase changes. Internal Energy U Internal energy is the total energy of all molecules in an object. Ideal Gas: U = < KE total > = N ½m<v 2 > U = 3 2 NkT N: total number of molecules k = 1.38 × 10 − 23 J (Boltzman constant) U = 3 2 nRT n: number of moles R = 8.314 J/mol K (universal gas constant) Heat We saw that energy is transferred due to a temperature difference. There is no work involved here. This transferred energy is called heat . Units: SI: J (Joules) cal (calorie) 1 cal = heat required to raise the temperature of 1 g of water from 14.5°C to 15.5°C Specific heat How much heat is needed to change by ΔT the temperature of a mass m of material X? = ∆ X Q mc T = X specific heat c water: c = 1 cal//(g °C) = 4186 J/(kg K) iron: c = 470 J/(kg K) c X does have some temperature dependence, but very small (ie, negligible for this course) Definition of calorie! Water has a very high specific heat. It’s “hard” to increase the temperature of water. Example: Kettle Your electric kettle is labeled 2000 W. Estimate how long it will take to boil enough water to fill your 0.5 liter thermos if water comes out of the tap at 15°C. Assuming that all the heat produced by the kettle is used to warm up the water, water water water Q m c T = ∆ Heat needed to warm up the water: Q water = ( 0.5 Liters 1 kg 1 Liter )( 4186 J kg ∘ C ) ( 100 − 15 ) ∘ C = 1.78 × 10 5 J t = Q P = 1.78 × 10 5 J 2000 W = 89 s = 1.5 min But of course in reality it will be a little longer. What are we But of course in reality it will be a little longer....
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 Summer '08
 B
 Thermodynamics, Energy, Heat

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