Phase Changes

Physics 102Professor Lee

CarknerLecture 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

Vi = 50 L /1000 L/m3 = 0.05 m3

Ti = 20 C +273.15 = 293.15 K P = (2 atm)(101300 Pa/atm) = 202600 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?

Vf = 40/1000 = 0.04 m3

Tf = 40 + 273.15 = 313.15 K PV= nRT, P = nRT/V Pf = (4.16)(8.31)(313.15) / (0.04) = 270637 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 upb) It goes downc) It stays the samed) It depends on the value of Re) 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 upb) It goes downc) It stays the samed) It depends on the value of Re) 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) TA = TB

B) TA = 2 TB

C) TA = ½ TB

D) TA = √2 TB

E) TA = (3/2) TB

How does the rms velocity of the molecules in room A compare to the rms velocity of the molecules in room B?

A) vA = vB

B) vA = 2 vB

C) vA = ½ vB

D) vA = √2 vB

E) vA = (3/2) vB

F) vA = (1/√2)vB

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 mcT 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)(Tf-(-10) + (0.1)(4186)(Tf-10) =0 Tf =

Wrong! Ice can’t be at greater than 0 C (0.01)(2090)(0-(-10)) +(0.01)(33.5X104)+ (0.01)(4186)(Tf-0)+(0.1)(4186)(Tf-

10) = 0 Tf =

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 Tf = 0 and solve for mmelt)

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: 15.1-15.3 Homework: Ch 14: P 25, 28, Ch 15: P

1, 2