Phase Changes Physics 102 Professor Lee Carkner Lecture 5
PAL #4 Kinetic Theory 50 liters of a gas at 20 C and 2 atm How many moles? PV=nRT, n = PV/RT Convert to SI units V i = 50 L /1000 L/m3 = 0.05 m 3 T i = 20 C = K P = (2 atm)( Pa/atm) = Pa n = (202600)(0.05) / (8.31)(293.15) = 4.16 moles
PAL #4 Kinetic Theory Compressed to 40 liters, temp raised to 40 C What will the new pressure be? V f = 40/1000 = 0.04 m 3 T f = = K PV= nRT, P = nRT/V P f = (4.16)(8.31)(313.15) / (0.04) = Pa Does this make sense? If you compress a gas and raise the temperature there are more molecule hitting each square meter and they have more energy so pressure should increase
If a fixed amount of gas at constant temperature undergoes a increase in volume, what happens to the pressure? a) It goes up b) It goes down c) It stays the same d) It depends on the value of R e) It depends on the number of moles
If a fixed amount of gas at constant pressure undergoes an increase in volume, what happens to the temperature? a) It goes up b) It goes down c) It stays the same d) It depends on the value of R e) It depends on the number of moles
Consider two rooms of a house, room A and room B. If the (otherwise identical) molecules in room B have twice as much average kinetic energy than the ones in A, how does the temperature of room A compare to the temperature of room B? A)T A = T B B)T A = 2 T B C)T A = ½ T B D)T A = √2 T B E)T A = (3/2) T B
How does the rms velocity of the molecules in room A compare to the rms velocity of the molecules in room B? A)v A = v B B)v A = 2 v B C)v A = ½ v B D)v A = √2 v B E)v A = (3/2) v B F)v A = (1/√2)v B
Phase Change Adding heat to ice will raise its temperature, but, Heat goes into phase change solid to liquid -- liquid to gas -- How much energy does this take? Represented by L
Heat of Fusion
Phase Change and Heat For liquid-solid change: For liquid-gas change: Amount of heat: Q = mL Adding heat will raise temperature only to a phase change point After that additional heat will go into phase change Note that you must make mL gained positive and mL lost negative
Heat and Temperature
Phase Change Calorimetry Need to include all of the mc T and mL terms for your calorimetry problem, but, Method: guess at the final result, if you get a non-physical result, try a different guess e.g. Can also do some quick initial computations to try and find the final state See
Melting Ice Cube Consider a 10 g ice cube at -10 C in 100 g of water at 10 C, what is final T? Assume ice does not melt (0.01)(2090)(T f -(-10) + (0.1)(4186)(T f -10) =0 T f = Wrong! Ice can’t be at greater than 0 C (0.01)(2090)(0-(-10)) +(0.01)(33.5X10 4 )+ (0.01)(4186)(T f - 0)+(0.1)(4186)(T f -10) = 0 T f = This T is OK since all that is left is water If we got a T less that 0 it would mean that only a fraction of the ice melted (set T f = 0 and solve for m melt )
Phase Change and Pressure Boiling point depends on both temperature and pressure Examples: In general lower external pressure means lower boiling point Easier for molecules to escape to vapor phase
Change in Boiling Point with Pressure
Phase Diagram Whether a substance is a solid, liquid or gas depends on the temperature and pressure Keeping T constant while increasing P usually produces a solid Ice is less dense than water This causes ice skates to melt ice and freezing water to expand and produce frost heaves
Phase Diagram
Phase Diagram Features Beyond the critical point there is no distinction between a liquid and gas Solid and liquid phases separated by a fusion curve Solid and gas phases separated by a sublimation curve
Velocity Distribution for Water
Evaporation How can water evaporate (become gas) if it is not at the boiling point? Evaporation only works if the air above is not saturated with vapor Since some of them will revert back to liquid This is why it is hard to cool off on humid days and easier on windy days
Next Time Read: Homework: Ch 14: P 25, 28, Ch 15: P 1, 2