Phase Changes

Physics 102Professor Lee

CarknerLecture 4

Session: 104884

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 inch and they have more energy so pressure should increase

Phase Change

Once ice starts to melt its temperature does not change.

solid to liquid -- melting How much energy does this take? Each substance has a latent heat

Represented by L

Heat and Temperature

Phase Change and Heat

heat of fusion

heat of vaporization Amount of heat:

Q = mL

Q = cmT

Q = mL Must add all heats together

Note that you must make mL gained positive and mL lost negative !

The Final State

Its hard to know what terms to put in your heat balance since you are not sure if you will get a phase change

e.g. liquid water at 120 C or ice at 5 C Can also do some quick initial computations to

try and find the final state

n.b., when a phase change happens, the specific heat changes e.g., once ice melts it becomes water

Phase Change Calorimetry

1. 2. Write down a “Q” for each heat

necessary to reach the final state3. Make sure you:

Write T = Tf –Ti

Assign a sign to each mL term Check units

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

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

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:

pressure cooker

Easier for molecules to escape to vapor phase

Change in Boiling Point with Pressure

Phase Diagram

Usually high P, low T produces a solid and low P, high T produces gas

Water is an exception, increasing pressure on ice produces water This causes ice skates to melt ice and freezing

water to expand and produce frost heaves

Beyond the critical point there is no distinction between a liquid and gas Just have a fluid

Liquid and gas phases separated by a vaporization 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 Pressure is too high

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

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