Chapter 17

SolidsPhase ChangesThermal Processes

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Vapor PressureThe pressure of the gas when it is in equilibrium with the liquid is called the equilibrium vapor pressure, and will depend on the temperature.A liquid boils at the temperature at which its vapor pressure equals the external pressure.

a) Charlottesvilleb) Denver (the mile high city)c) the same in both placesd) Ive never cooked in Denver, so I really dont knowe) you can boil potatoes? Boiling PotatoesWill boiled potatoes cook faster in Charlottesville or in Denver?

a) Charlottesvilleb) Denver (the mile high city)c) the same in both placesd) Ive never cooked in Denver, so I really dont knowe) you can boil potatoes? Boiling PotatoesWill boiled potatoes cook faster in Charlottesville or in Denver?The lower air pressure in Denver means that the water will boil at a lower temperature... and your potatoes will take longer to cook.

Phase DiagramThe vapor pressure curve is only a part of the phase diagram.When the liquid reaches the critical point, there is no longer a distinction between liquid and gas; there is only a fluid phase.There are similar curves describing the pressure/temperature of transition from solid to liquid, and solid to gas

Fusion CurveThe fusion curve is the boundary between the solid and liquid phases; along that curve they exist in equilibrium with each other.

One of these two fusion curves has a shape that is typical for most materials, but the other has shape specific to water.

Which is which?(a) Curve 1 is the fusion curve for water(b) Curve 2 is the fusion curve for water(c) Trick question: there is no fusion curve for water!

Fusion CurveThe fusion curve is the boundary between the solid and liquid phases; along that curve they exist in equilibrium with each other.

One of these two fusion curves has a shape that is typical for most materials, but the other has shape specific to water.

Which is which?(a) Curve 1 is the fusion curve for water(b) Curve 2 is the fusion curve for water(c) Trick question: there is no fusion curve for water!

Ice melts under pressure!This is how an ice skate works

Phase EquilibriumThe sublimation curve marks the boundary between the solid and gas phases. The triple point is where all three phases are in equilibrium.

Heat and Phase ChangeWhen two phases coexist, the temperature remains the same even if a small amount of heat is added. Instead of raising the temperature, the heat goes into changing the phase of the material melting ice, for example.

Latent HeatThe heat required to convert from one phase to another is called the latent heat.The latent heat, L, is the heat that must be added to or removed from one kilogram of a substance to convert it from one phase to another. During the conversion process, the temperature of the system remains constant.

Latent HeatThe latent heat of fusion is the heat needed to go from solid to liquid; the latent heat of vaporization from liquid to gas.

Boiling PotatoesWill potatoes cook faster if the water is boiling faster? a) Yesb) Noc) Wait, Im confused. Am I still in Denver?

Boiling PotatoesWill potatoes cook faster if the water is boiling faster? The water boils at 100C and remains at that temperature until all of the water has been changed into steam. Only then will the steam increase in temperature. Because the water stays at the same temperature, regardless of how fast it is boiling, the potatoes will not cook any faster.Follow-up: How can you cook the potatoes faster?YesNoc) Wait, Im confused. Am I still in Denver?

Youre in Hot Water!Which will cause more severe burns to your skin: 100C water or 100C steam?a) waterb) steam c) both the same d) it depends...

Although the water is indeed hot, it releases only 1 cal/(gK) of heat as it cools. The steam, however, first has to undergo a phase change into water and that process releases 540 cal/g, which is a very large amount of heat. That immense release of heat is what makes steam burns so dangerous.Youre in Hot Water!Which will cause more severe burns to your skin: 100C water or 100C steam?a) waterb) steam c) both the same d) it depends...

Phase Changes and Energy ConservationSolving problems involving phase changes is similar to solving problems involving heat transfer, except that the latent heat must be included as well.

Water and Ice You put 1 kg of ice at 0C together with 1 kg of water at 50C. What is the final temperature? LF = 80 cal/gcwater = 1 cal/g Ca) 0Cb) between 0C and 50C c) 50C d) greater than 50C

How much heat is needed to melt the ice? Q = mLf = (1000 g) (80 cal/g) = 80,000 cal

How much heat can the water deliver by cooling from 50C to 0C? Q = cwater m T = (1 cal/g C) (1000 g) (50C) = 50,000 cal Thus, there is not enough heat available to melt all the ice!!Water and Ice You put 1 kg of ice at 0C together with 1 kg of water at 50C. What is the final temperature? LF = 80 cal/gcwater = 1 cal/g Ca) 0Cb) between 0C and 50C c) 50C d) greater than 50C

a) Add more ice to the icewater b) add salt to the icewaterc) hold the icewater in an evacuated chamber (vacuum) d) Jump in the car and drive to a nearby convenience store Ice Cold Root BeerYou have neglected to chill root beer for your sons 5th-birthday party. You submerge the cans in a bath of ice and water as you start dinner. How can you hurry the cooling process?

a) Add more ice to the icewater b) add salt to the icewaterc) hold the icewater in an evacuated chamber (vacuum) d) Jump in the car and drive to a nearby convenience store Ice Cold Root BeerYou have neglected to chill root beer for your sons 5th-birthday party. You submerge the cans in a bath of ice and water as you start dinner. How can you hurry the cooling process?Not a), because ice water at 1 atm is zero degrees, no matter the proportion of water and iceNot c), because ice is less dense than water so you will raise the melting point when you reduce the pressure. This will allow the water to get a little warmer than 0oNot d), because youll forget your wallet and it will end up taking more timeb) because salt interferes with the formation of ice. This barrier to the solid phase lowers the fusion temperature, and so reduces the temperature of the ice water. (This is why you salt the sidewalk in winter.)

remember: water is weird: it melts under pressure, and freezes under vacuum, when near the fusion curveAgain: explaining why putting the ice/water under vacuum wont help the root beer chill faster

As pressure goes lower, the ice/water mixture will ride the fusion curve from point 1 to point 2.This implies that temperature goes up.The larger T, the more heat transfers per unit time. Thus, the colder the ice bath, the faster the root beer will chill, and the warmer the bath, the slower the root beer will chillWhen two states exist in the same system (like, ice and water), the system MUST be on the equilibrium curve (in the case, the fusion curve).

Chapter 18The Laws of Thermodynamics

Reversible (frictionless pistons, etc.) and quasi-static processesFor a process to be reversible, it must be possible to return both the system and its surroundings to the same states they were in before the process began.Quasi-static = slow enough that system is always effectively in equilibriumarea under the curveW =

a) zero b) -153 Jc) -41 J d) -26 Je) 41 J Internal EnergyAn ideal gas is taken through the four processes shown. The changes in internal energy for three of these processes is as follows:

The change in internal energy for the process from C to D is:

Internal Energya) zero b) -153 Jc) -41 J d) -26 Je) 41 JAn ideal gas is taken through the four processes shown. The changes in internal energy for three of these processes is as follows:

The change in internal energy for the process from C to D is:PV = nRTso in a PV cycle, T = 0T = 0 means that U = 0UCD = -41 J

How much work is done by the gas in this process, in terms of the initial pressure and volume?One mole of an ideal monatomic gas undergoes the reversible expansion shown in the figure, where V2 = 5 V1 and P2 = 3 P1.a) 4 P1V1b) 7 P1V1 c) 8 P1V1 d) 21 P1V1 e) 29 P1V1

a) 4 P1V1b) 7 P1V1 c) 8 P1V1 d) 21 P1V1 e) 29 P1V1How much work is done by the gas in this process, in terms of the initial pressure and volume?One mole of an ideal monatomic gas undergoes the reversible expansion shown in the figure, where V2 = 5 V1 and P2 = 3 P1.Area under the curve:(4 V1)(P1) + 1/2 (4V1)(2P1) = 8 V1P1

How much internal energy is gained by the gas in this process, in terms of the initial pressure and volume?One mole of an ideal monatomic gas undergoes the reversible expansion shown in the figure, where V2 = 5 V1 and P2 = 3 P1.a) 7 P1V1b) 8 P1V1 c) 15 P1V1 d) 21 P1V1 e) 29 P1V1

How much internal energy is gained by the gas in this process, in terms of the initial pressure and volume?One mole of an ideal monatomic gas undergoes the reversible expansion shown in the figure, where V2 = 5 V1 and P2 = 3 P1.a) 7 P1V1b) 8 P1V1 c) 15 P1V1 d) 21 P1V1 e) 29 P1V1Ideal monatomic gas: U = 3/2 nRTIdeal gas law: PV = nRTP2V2 = 15 P1V1 (PV) = 14 P1V1U = 3/2 PVU = 21 P1V1

How much heat is gained by the gas in this process, in terms of the initial pressure and volume?One mole of an ideal monatomic gas undergoes the reversible expansion shown in the figure, where V2 = 5 V1 and P2 = 3 P1.a) 7 P1V1b) 8 P1V1 c) 15 P1V1 d) 21 P1V1 e) 29 P1V1

How much heat is gained by the gas in this process, in terms of the initial pressure and volume?One mole of an ideal monatomic gas undergoes the reversible expansion shown in the figure, where V2 = 5 V1 and P2 = 3 P1.a) 7 P1V1b) 8 P1V1 c) 15 P1V1 d) 21 P1V1 e) 29 P1V1First Law of ThermodynamicsW = 8 P1V1

a) at constant pressure b) if the pressure increases in proportion to the volumec) if the pressure decreases in proportion to the volumed) at constant temperaturee) adiabatically Internal EnergyAn ideal gas undergoes a reversible expansion to 2 times its original volume. In which of these processes does the gas have the largest loss of internal energy?

a) at constant pressure b) if the pressure increases in proportion to the volumec) if the pressure decreases in proportion to the volumed) at constant temperaturee) adiabatically Internal EnergyAn ideal gas undergoes a reversible expansion to 2 times its original volume. In which of these processes does the gas have the largest loss of internal energy?Since U = 3/2 nRT, and PV=nRT, the largest loss in internal energy corresponds to the largest drop in temperature, and so the largest drop in the product PV.a) PV doubles. Ufinal = 2Uinitialb) (PV)final = 4 (PV)initial Ufinal = 4Uinitialc) PV is constant, so U is constantd) U is constante) Adiabatic, so U = -W. This is the only process which reduces U!

Specific Heat for an Ideal Gas at Constant VolumeSpecific heats for ideal gases must be quoted either at constant pressure or at constant volume. For a constant-volume process,

For an ideal gas (from the kinetic theory)First Law of ThermodynamicsConstant Volume

Specific Heat for an Ideal Gas at Constant PressureAt constant pressure, (some work is done)Some of the heat energy goes into the mechanical work, so more heat input is required to produce the same T

For an ideal gas (from the kinetic theory)First Law of Thermodynamics

Specific Heats for an Ideal GasAlthough this calculation was done for an ideal, monatomic gas, the difference Cp - Cv works well for real gases.Both CV and CP can be calculated for a monatomic ideal gas using the first law of thermodynamics.

Specific Heats and Adiabats In Ideal GasThe P-V curve for an adiabat is given by for monotonic gases

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Answer: bAnswer: a