ap physics 2 unit 2: thermodynamics name: “we cannot … · zero hour in class homework ... extra...

AP Physics 2 Unit 2: Thermodynamics Name:_________________________ “We cannot teach people anything. We can only help them discover it within themselves.” Galileo

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Date

Zero Hour In Class Homework (to be done that night or

before coming to the next class

period)

Thurs 9/1

Fluids Test Watch Thermo video 1. Thermal

Energy, Heat, and Temperature. Fill

out WSQ google form

Mon 9/5 `

NO SCHOOL

Tue 9/6

Gas properties

simulation: PHET gas

lab 1

Discuss Video 1: heat vs.

temp, probability

distributions, work on packet

Watch Thermo video 2. Heat Transfer

and Thermal Equilibrium. Fill out

WSQ google form

Thurs 9/8

Discuss video 2: heat

transfer and thermal

conductivity

Watch Thermo video 3. Pressure,

Force and the Ideal Gas Law. Fill out

WSQ google form

Mon 9/12

LSM

Discuss video 3: the role of

collisions on force and

pressure and the Ideal Gas

Law and work on problems

Watch Thermo video 4. PV diagrams.

Fill out WSQ google form

Tue 9/13

Boyles Law Lab Discuss video 4: what’s up

with PV diagrams

Watch Thermo video 5. The first law

of thermodynamics. Fill out WSQ

google form

Thurs 9/15

Discuss video 5: First Law

and how it compliments PV

diagrams

Mon 9/19

Quiz on Force Pressure

and the Ideal gas law.

Work on more PV problems

Tues 9/20

Thermo. PHET lab Work on more PV problems Watch Thermo video 6. The Second

Law of thermodynamics and Entropy.

Fill out WSQ google form

Thurs 9/22

Quiz on PV Diagrams

Discuss video 6 Entropy

Mon 9/26

LSM

Homecoming

week

Final Questions on

Thermodynamics

Tues 9/27

NO Lab, but optional

extra help session

before test.

Thermo Test


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Video 1. Internal Energy of a System, Temperature and Kinetic Energy

Textbook: 11.3 page 327-328 & 12.2 pages 359- 361

Objectives: 1. The internal energy of a system includes the kinetic energy of the objects that make up the system and the

potential energy of the configuration of the objects that make up the system.

The student is able to describe and make predictions about the internal energy of systems.

The student is able to calculate changes in kinetic energy and potential energy of a system, using

information from representations of that system.1

2. The temperature of a system characterizes the average kinetic energy of its molecules. a. The average kinetic

energy of the system is an average over the many different speeds of the molecules in the system that can be

described by a distribution curve. b. The root mean square speed corresponding to the average kinetic energy

for a specific gas at a given temperature can be obtained from this distribution.

The student is able to qualitatively connect the average of all kinetic energies of molecules in a system to

the temperature of the system.

The student is able to connect the statistical distribution of microscopic kinetic energies of molecules to the

macroscopic temperature of the system and to relate this to thermodynamic processes.

Guided notes for video 1 Questions

Define thermal energy.

What are the two mechanisms for energy to change in a system?

What is the difference between heat and temperature?

What is the equation that relates kinetic energy to temperature?

What equation relates internal energy (thermal energy) of a system to the temperature of the system? - In terms of molecules: - In terms of moles:

What is a Maxwell-Boltzmann probability distribution and how does it relate to molecular speeds?


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What is Vrms and why do we need to use it when we are calculating the kinetic energy of a sample of gas.

What is the equation for Vrms in terms of temperature?

How does the Maxwell Speed Distribution graph vary for molecules of different masses?

What is absolute zero?

Practice problems in video (pause video and try these problems)

Calculate the internal energy (U) of one mole of hydrogen at a 300 K.

Calculate the rms speed of a Nitrogen molecule (N2) when the temperature is 100 oC

Summarize: on the google WSQ form for this video summarize what you learned. Make sure you discuss the differences between heat and temperature and how they relate the internal energy of the system.

Practice Questions: show work below and enter answer onto google form 1. A large bedroom contains about 1x107 molecules of air. How much energy is required to raise the

temperature of the air in the room by 5C.

2. Most of the earth’s atmosphere is nitrogen (N2). The coldest every observed on earth was -129C. What is the vrms speed of nitrogen at this temperature? (note: you need to convert the molar mass of nitrogen in atomic mass units from the periodic table into kilograms…see the pink sheet for the conversion)


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Video 2. Heat transfer and Thermal Equilibrium. Textbook: 11.3 pages 329-330 and 12.8 pages 383-388 Objectives: 1. Energy is transferred spontaneously from a higher temperature system to a lower temperature system. The

process through which energy is transferred between systems at different temperatures is called heat. a.

Conduction, convection, and radiation are mechanisms for this energy transfer. b. At a microscopic scale the

mechanism of conduction is the transfer of kinetic energy between particles. c. During average collisions

between molecules, kinetic energy is transferred from faster molecules to slower molecules.

The student is able to make predictions about the direction of energy transfer due to temperature differences

based on interactions at the microscopic level.

2. Energy can be transferred by thermal processes involving differences in temperature; the amount of energy

transferred in this process of transfer is called heat.

The student is able to describe the models that represent processes by which energy can be transferred

between a system and its environment because of differences in temperature: conduction, convection, and

radiation.

3. The approach to thermal equilibrium is a probability process. a. The amount of thermal energy needed to

change the temperature of a system of particles depends both on the mass of the system and on the temperature

change of the system. b. The details of the energy transfer depend upon interactions at the molecular level. c.

Since higher momentum particles will be involved in more collisions, energy is most likely to be transferred

from higher to lower energy particles. The most likely state after many collisions is that both systems of

particles have the same temperature.

The student is able to construct an explanation, based on atomic scale interactions and probability, of how a

system approaches thermal equilibrium when energy is transferred to it or from it in a thermal process.

4. Matter has a property called thermal conductivity. a. The thermal conductivity is the measure of a material’s

ability to transfer thermal energy.

The student is able to design an experiment and analyze data from it to examine thermal conductivity.


Why do hot things get cold (and cold things get hot)?

In what direction does heat flow?

Define thermal equilibrium.

What is the zeroth law of thermodynamics?

After watching the simulation, explain why heat flows from hot to cold.


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From the simulation: Predict the final temperature when a 750K sample of a 100 particles combine with 100 particles at 150K: In simulation 2 when 200 particles at 750K combine with 50 particles at 150K will the final temperature be the same as the first simulation? Why or why not?

What is conduction? Give an example.

What is the equation for heat transfer by conduction

What are some examples of good thermal conductors? What are some examples of materials with low values for thermal conductively?

Pause the video and Solve: A window has a glass surface of 1.6 x 103 cm2 and a thickness of 3.0 mm. a) Find the rate of heat transfer by conduction through this pane when the temperature of the inside surface of the glass is 20 oC and the outside temperature is 40oC. B) How much flows through per hour?

What is heat transfer by convection? Give an example.

What is heat transfer by radiation? Give an example.

Summary: Summarize what you learned on the google form for this video. Include how heat transfers and why it always goes from hot to cold. Also discuss the differences in the three methods of heat transfer.

Practice Problems: show work below and enter answer onto google form

1. A glass window pane is 2.7 m high, 2.4 m wide, and 9.0 mm thick. The temperature at the inner surface of

the glass is and at the outer surface 4°C. How much heat is lost each hour through the window?

2. The process in which heat flows by the mass movement of molecules from one place to another is known

as A) conduction. B) convection. C) radiation.

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J 84.0

mk


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Video 3. Pressure, force, and the Ideal gas law. Textbook: 12.2 pages 362 – 366. Objectives:

The pressure of a system determines the force that the system exerts on the walls of its container and is a measure of

the average change in the momentum or impulse of the molecules colliding with the walls of the container. The

pressure also exists inside the system itself, not just at the walls of the container.

The student is able to make claims about how the pressure of an ideal gas is connected to the force exerted

by molecules on the walls of the container, and how changes in pressure affect the thermal equilibrium of

the system.

Treating a gas molecule as an object (i.e., ignoring its internal structure), the student is able to analyze

qualitatively the collisions with a container wall and determine the cause of pressure, and at thermal

equilibrium, to quantitatively calculate the pressure, force, or area for a thermodynamic problem given two

of the variables.

In an ideal gas, the macroscopic (average) pressure (P), temperature (T), and volume (V), are related by the equation

PV nRT.

The student is able to extrapolate from pressure and temperature or volume and temperature data to make

the prediction that there is a temperature at which the pressure or volume extrapolates to zero.

The student is able to design a plan for collecting data to determine the relationships between pressure,

volume, and temperature, and amount of an ideal gas, and to refine a scientific question concerning a

proposed incorrect relationship between the variables.

The student is able to analyze graphical representations of macroscopic variables for an ideal gas to

determine the relationships between these variables and to ultimately determine the ideal gas law PV nRT.


What are some assumptions we need to make when using the ideal gas law?

What causes pressure?

What would be necessary to have a pressure of zero (a complete vacuum)?

How does increasing temperature effect pressure and why?

How does increasing volume effect pressure and why?


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How does increasing the amount of molecules of a gas effect pressure and why?

What is the ideal gas law and what units must be used for each variable (when using the constant 8.31)?

Quick Check 12.10: Two identical cylinders, A and B, contain the same type of gas at the same pressure. Cylinder A has twice as much gas as cylinder B. Which is true about their temperatures?

Quick Check 12.11: Two cylinders, A and B, contain the same type of gas at the same temperature. Cylinder A has twice the volume as cylinder B and contains half as many molecules as cylinder B. Which is true of their pressures?

Practice Problems in the video: What will be its final temperature in Celsius if the gas at 0.20 x 105 Pa is compressed to 0.70 m3 and the absolute pressure increases to 0.80 x 105 Pa? If 2.0 mol of an ideal gas are confined to a 5.0 L vessel at a pressure of 8.0 x 105 Pa, what is the average kinetic energy of a gas molecule?

Summary: Write a summary of what you learned from the video on the WSQ google form. Include what causes pressure and how you can change the pressure of a gas.

Practice Problems: show work below and enter answer onto google form 1. How would the pressure of an ideal gas change if the and the volume of the gas and vrms speed of the molecules were both doubled? 2. What volume, in m3, is occupied by 18 moles of an ideal gas at a pressure of 1.3 atm and a temperature of 0°C?


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Video 4. PV Processes Textbook 12.3 pages 366-372 Objectives: The first law of thermodynamics is a specific case of the law of conservation of energy involving the internal energy

of a system and the possible transfer of energy through work and/or heat. Examples should include P-V diagrams —

isovolumetric process, isothermal process, isobaric process, adiabatic process. No calculations of heat or internal

energy from temperature change; and in this course, examples of these relationships are qualitative and/or semi-

quantitative.

The student is able to predict qualitative changes in the internal energy of a thermodynamic system

involving transfer of energy due to heat or work done and justify those predictions in terms of conservation

of energy principles.

The student is able to create a plot of pressure versus volume for a thermodynamic process from given data.

The student is able to use a plot of pressure versus volume for a thermodynamic process to make

calculations of internal energy changes, heat, or work, based upon conservation of energy principles (i.e.,

the first law of thermodynamics).


What is a PV diagram?

What is an isovolumetric process? Give an example of how you could create an isochoric process in the lab?

Sketch and label an isovolumetric process on the PV diagram below originating at the dot:

Quick Check 12.12: The temperature of a rigid (i.e., constant-volume), sealed container of

gas increases from 100C to 200C. The gas pressure increases by a factor of:

What is an isobaric process? Give an example of how you could create an isobaric process in the lab?

Sketch and label an isobaric process on the PV diagram above (with the isovolumetric process).


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What is an isothermal process? Give an example of how you could create an isothermal process in the lab?

Sketch an isothermal process on the PV diagram on the previous page.

What is an adiabatic process? Give an example of an adiabatic process.

How is the PV diagram of an adiabatic process different from an isothermal process?

Quick Check 12.14: A cylinder of gas has a frictionless but tightly sealed piston of mass M. A small flame heats the cylinder, causing the piston to slowly move upward. For the gas inside the cylinder, what kind of process is this? Quick Check 12.16: A cylinder of gas floats in a large tank of water. It has a frictionless but tightly sealed piston of mass M. Small masses are slowly placed onto the top of the piston, causing it to slowly move downward. For the gas inside the cylinder, what kind of process is this? Quick Check 12.19: A sample of gas is in a cylinder with a moveable piston. The force on the piston can be varied, altering the pressure and volume. A sample of gas is taken from an initial state to a final state following a curve on the pV diagram shown. The final temperature is? Quick Check 12.20: A sample of gas is in a cylinder with a moveable piston. The force on the piston can be varied, altering the pressure and volume. A sample of gas is taken from an initial state to a final state following a curve on the pV diagram shown. The final temperature is?

Practice Problems in video: (Pause video and try to solve) An ideal gas initially has pressure Po, at volume Vo and absolute temperature To. It then undergoes the following series of processes (as shown in the diagram): Find the temperature at each end point in terms of To


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One mole of an ideal gas is taken through step A to B so that its pressure drops from 2.2 to 1.4 atm. Then from B to C the gas expands from 0.0068 to 0.0107 m3, where the temperature reaches it's original value. a. What type of process is A to B?

B to C?

b. Calculate the temperatures at A, B &C:

Summary: Summarize what you learned in the video on the WSQ google form. Include information about the different type of PV processes.

Practice Problems: show work below and enter answer onto google form 1. A gas follows the process shown to the right. What is the final-to-initial temperature ratio Tf /Ti? 2. A sample of gas is in a cylinder with a moveable piston. The force on the piston can be varied, altering the pressure and volume. A sample of gas is taken from an initial state to a final state following a curve on the pV diagram shown. The final temperature is

A. Higher than the initial temperature. B. The same as the initial temperature.

C. Lower than the initial temperature.


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Video 5. 1st Law of Thermodynamics

Textbook 11.4 pages 330-331 and 12.3 pages 369-370

Objectives: Energy can be transferred by an external force exerted on an object or system that moves the object or system

through a distance; this energy transfer is called work. Energy transfer in mechanical or electrical systems may

occur at different rates. Power is defined as the rate of energy transfer into, out of, or within a system.

The student is able to make claims about the interaction between a system and its environment in which the

environment exerts a force on the system, thus doing work on the system and changing the energy of the

system (kinetic energy plus potential energy).

The student is able to predict and calculate the energy transfer to (i.e., the work done on) an object or

system from information about a force exerted on the object or system through a distance.

The student is able to design an experiment and analyze graphical data in which interpretations of the area

under a pressure-volume curve are needed to determine the work done on or by the object or system.


What is the first law of thermodynamics? What is the mathematical equation that represents it?

Explain the difference between positive and negative heat.

What is the equation for calculating work done on a gas?

Explain positive and negative work in terms of expansion and compression and how that changes the energy of the gas.

How can you use a PV diagram to determine the amount of work done on a gas?

What type of isoprocess always has zero work done on or by the gas?


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Practice Problems in the video: Using the PV diagram:

- Find the work done in each process and the net work done by the gas in terms of Po and Vo

- What is the net change in internal energy of the gas during the entire process and

WHY?

One mole of an ideal gas is taken through step A to B so that its pressure drops from 2.2 to 1.4 atm. Then from B to C the gas expands from 0.0068 to 0.0107 m3, where the temperature reaches it's original value. The gas is then taken through an isothermal process back to its original state, A.

a. Calculate the work done on the gas from A to B

B to C

b. Is the net work (from A to B to C to A) positive, negative, or zero?

c. Is total change in internal energy of the gas from A to C positive, negative, or

zero?

d. Is the total heat flow from A to C positive, negative, or zero?

Summary: Summarize what you learned on the google form. Include a description of the first law of thermodynamics and how you can use PV diagrams to determine how much work is done and about heat flow.

Practice Problems: show work below and enter answer onto google form For the PV diagram shown below:

1. Is the net work done on the gas in the process positive, negative, or zero?

2. Is the net change in internal energy positive, negative, or zero?

3. Is the net heat flow positive, negative, or zero?

P

V

a

10 Pa

75 Pa

0.0050 m 0.050 m3 3

P

V

a

bc

10 Pa

75 Pa

0.0050 m 0.050 m3 3


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Video 6. 2nd Law of Thermodynamics

Textbook: 11.7- 11.8, pages 337-342

Objectives:

The second law of thermodynamics describes the change in entropy for reversible and irreversible

processes. Only a qualitative treatment is considered in this course.

a. Entropy, like temperature, pressure, and internal energy, is a state function, whose value depends only

on the configuration of the system at a particular instant and not on how the system arrived at that

configuration. b. Entropy can be described as a measure of the disorder of a system, or of the

unavailability of some system energy to do work. c. The entropy of a closed system never decreases, i.e.,

it can stay the same or increase. d. The total entropy of the universe is always increasing.

The student is able to connect qualitatively the second law of thermodynamics in terms of the state

function called entropy and how it (entropy) behaves in reversible and irreversible processes.


What are some examples of spontaneous processes?

How did the ping pong balls illustrate that microscopic processes are reversible but macroscopic processes are irreversible?

Go back to the definition of thermal equilibrium from our second video on heat transfer. Explain why thermal equilibrium is the most probable state.

What is Entropy?

What is the Second Law of Thermodynamics?

Why is the conversion from mechanical energy to thermal energy an irreversible process?


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What is a heat engine?

How is work calculated for a heat engine?

Why can’t heat engines ever be 100% efficient?

What is an example of a heat engine?

What is a heat pump?

Summary: on the google form summarize what you learned in this video about the second law of thermodynamics and entropy.


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In Class Practice: Video 1. Temperature, Kinetic Energy and Speed: 1. What is the average kinetic energy of atoms at absolute zero? 2. Can an atom have negative kinetic energy? Why or why not? 3. Is it possible to have a temperature less than absolute zero? Why or why not? 4. Do each of the following describe a property of a system, and interaction of a system with its environment or both? Explain. a. Temperature: b. Heat: c. Thermal Energy: 5. .Consider 2 gases, A and B, each in a 1.0 L container with both gases at the same temperature and pressure.

The mass of gas A in the container is 0.25 g and the mass of gas B in the container is 0.51 g. a. Which gas sample has the most molecules present?

b. Which gas sample has the largest average kinetic energy?

c. Which gas sample has the fastest average velocity?

d. How can the pressure in the 2 containers be equal to each other since the larger gas B molecules collide with the container walls more forcefully?

6. What is the average kinetic energy per molecule of a tank of oxygen gas at 25.0 C? (6.17x10-21 J)


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7. A rigid container holds both hydrogen gas (H2) and nitrogen gas (N2) at 100C. How do their rms speeds compare?

8. If you double the temperature of a gas.

a. Does the rms speed of the atoms increase by a factor of √2, 2 or 22? Explain.

b. Does the average kinetic energy of the atoms increase by a factor of √2, 2 or 22? Explain. 9. Suppose you could suddenly increase the speed of every atom in a gas by a factor of 2.

a. Would the rms speed of the atoms increase by a factor of √2, 2 or 22? Explain.

b. Would the thermal energy o the gas increase by a factor of √2, 2 or 22? Explain.

c. Would the temperature of the gas increase by a factor of √2, 2 or 22? Explain. 10. Air is primarily a mixture of nitrogen (N2) and oxygen (O2). Assume that each behaves as an ideal gas and

determine the rms speeds of each molecule when the temperature in air is 293K. (N = 511 m/s O = 478 m/s) 11. True or False in regards to the Maxwell-Boltzmann distribution. Explain your answer.

a. The distributions are symmetrical

b. The more massive the particle the faster the velocities.

c. The lower the temperature the slower the average velocity.

d. Broader distributions are caused by higher temperatures and heavier particles.


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12. For the molecular speed distribution graph shown to the right: a. How are samples A, B, and C the same and how are they

different?

b. If each sample contains the same number of molecules why are their peak heights different?

13. The speed distribution of a sample of a monoatomic gas is shown below. If the gas is heated, draw on the

graph the new molecular speed distribution of the sample. If the sample is cooled, draw on the graph the new molecular speed distribution.


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Video 2. Heat Transfer

14. An architect is interested in estimating the rate of

heat loss, ΔQ/Δt, through a sheet of insulating

material as a function of the thickness of the sheet.

Assuming fixed temperatures on the two faces of the

sheet and steady state heat flow, which one of the

graphs shown in the figure best represents the rate of

heat transfer as a function of the thickness of the

insulating sheet?

A) A B) B C) C D) D E) E 15. Heat flows through a cylindrical copper bar at the rate of 100W. A second cylindrical copper bar between the

same two temperatures is twice as long and has twice the diameter as the first bar. What is the rate of heat flow through the second bar?

16. The thermal conductivity of wood and concreate are 0.2 W/m K and 0.8 W/m K, respectively. Suppose your house has 1 inch thick wood siding on the outside. You would like to replace the wood siding with a concrete exterior wall. What thickness must the concrete have to provide the same insulation value as the wood? Explain.

17. A titanium cube at 400K radiates 50W of heat. How much heat does the cube radiate if tis temperature is

increased to 800K?

18. A single pane window is 25 mm thick. It measures 1.2 m by 2.5 m. One side of the window is 25C and the other

side is -22C. How much heat is lost through the window in 24 hours? (Kglass = 0.84 J/s m °C)? (4.1x108 J) 19. A 1.8 cm thick wood floor covers a 4.0 x 5.5 m room. The subfloor on which the flooring sits is at a

temperature of 16.2C, while the air in the room is at 19.6C. What is the rate of heat conduction through the floor (kwood=0.1 J/s m °C)? (416 J/s)


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Video 3. Pressure, Force, and the Ideal Gas Law. 20.


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21. A gas is held in a sealed container from which no molecules can enter or leave. Suppose the absolute

temperature T of the gas is doubled. Will the gas pressure double? Why or why not can you draw this conclusion?

22. Consider an ideal gas contained in a confined volume. How would the pressure of the gas change if a. the number of molecules of the gas were doubled, without changing the container or the temperature?

b. the volume of the container were doubled, without changing the number of molecules or the temperature?

c. the temperature (in K) of the gas were doubled, without changing the number of molecules or the volume of the container?

d. the rms speed of the molecules were doubled, without changing the number of molecules or the volume of the container?

23. When you stifle a sneeze, you can damage delicate tissues because the pressure of the air that is not allowed

to escape may rise by up to 45 kPa. If this extra pressure acts on the inside of you 8.4 mm diameter eardrum, what is the outward force? (2.5 N)

24. A scuba tank contains 2.35 L of air at 22.1C and 1.00 atm (101.3 kPa). What is the pressure in the tank if the

temperature is increased to 128C? (137.5 kPa)

25. A tank holds 2.85 L of oxygen at 22.1C and 235 atm. (a) How many moles of gas does the tank contain? (27.7 moles) (b) What is the average kinetic energy per molecule? (6.11x10-21 J)


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26. 2005B6 An experiment is performed to determine the number n of moles of an ideal gas in

the cylinder shown above. The cylinder is fitted with a movable, frictionless piston of area A. The piston is in equilibrium and is supported by the pressure of the gas. The gas is heated while its pressure P remains constant. Measurements are made of the temperature T of the gas and the height H of the bottom of the piston above the base of the cylinder and are recorded in the table below. Assume that the thermal expansion of the apparatus can be ignored. a. Write a relationship between the quantities T and H, in terms of the given quantities and fundamental constants, that will allow you to determine n. b. Plot the data on the axes below so that you will be able to determine n from the relationship in part (a). Label the axes with appropriate numbers to show the scale.

c. Using your graph and the values A = 0.027 m2 and P = 1.0 atmosphere, determine the experimental value of n.

Above answers: a) H= nRT/PA c) slope is H/T so slope * PA/R = between 0.98 – 1.11 mole


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Video 4 PV Processes 27. The graphs below use a dot to show the initial state of a gas. Draw a pV diagram showing the following

processes:

28. Interpret the pV diagrams shown below by a. Naming the process. b. Stating the factors by which p, V, and T change. (a fixed quantity changes by a factor of 1)

29. Starting from the initial state shown, draw a pV diagram for the three-step process: a. A constant-volume process that halves the temperature. b. An isothermal process that halves the pressure, then c. An isobaric process that doubles the volume.

Label each of the stages on your diagram.


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30. How much work is done by the gas in each of the following processes?

31. The figure shows a process in which work is done to compress a gas. a. Draw and label a process A that starts and ends at the same

points but does more work on the gas. b. Draw and label a process B that starts and ends at the same

points but does less work on the gas.

32. Starting from the point shown, draw a pV diagram for the following processes.


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Video 6. 1st Law of Thermodynamics


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27


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33. A thermodynamic system is taken from an initial state X along the path XYZ X as shown in the PV-diagram to the below.

a. For the process X Y , U is greater than zero and (A) Q < 0 and W = 0 (B) Q < 0 and W > 0 (C) Q > 0 and W < 0 (D) Q > 0 and W = 0 (E) Q > 0 and W > 0

b. For the process Y Z , Q is greater than zero and

(A) W < 0 and U = 0

(B) W = 0 and U < 0

(C) W = 0 and U > 0

(D) W > 0 and U = 0

(E) W > 0 and U > 0

34. A gas undergoes a thermodynamic expansion process as shown. Process ab represents the output work,

process bc represents input work, all three processes involve heat transfer. a. what is the work accomplished along path ca? (0)

b. What is the work along path ab? (-1.9 J)

c. What is the work along path bc? (+0.45 J)

d. What is the net work for the entire thermo cycle? (-1.46 J)

35. For each of the following process:

P

V

a

10 Pa

75 Pa

0.0050 m 0.050 m3 3

P

V

a

bc

10 Pa

75 Pa

0.0050 m 0.050 m3 3


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36. One mole of an ideal gas is confined to a container with a movable piston. The questions below refer to the

processes shown on the PV diagram to the right. Process I is a change from state X to state Y at constant

pressure. Process II is a change from state W to state Z at a different constant pressure.

37. (2008B5) A 0.03 mol sample of helium is taken through the cycle shown in the diagram to the right. The temperature of state A is 400 K. a. For each process in this cycle, indicate in the table below whether the quantities

W, Q, and ΔU are positive (+), negative (-), or zero (0). W is the work done on the helium sample.

b. Explain your response for the signs of the quantities for process

c. Calculate Vc.


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38.

AP Physics 2 Unit 2: Thermodynamics Name:_________________________

For these AP Problems the answers are at the end

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39. 2006B5 A cylinder with a movable frictionless piston contains an ideal gas that is initially in state 1 at 1 x 105 Pa, 373 K, and 0.25 m3. The gas is taken through a reversible thermodynamic cycle as shown in the PV diagram to the right. a. Calculate the temperature of the gas when it is in the following

states. i. State 2

ii. State 3

b. Calculate the net work done on the gas during the cycle.

c. Was heat added to or removed from the gas during the cycle? Added ______ Removed ______ Neither added nor removed

Justify your answer.

40. 2007B5. The figure above shows a 0.20 m diameter cylinder fitted with a frictionless piston, initially fixed in place. The cylinder contains 2.0 moles of nitrogen gas at an absolute pressure of 4.0 x 105 Pa . Nitrogen gas has a molar mass of 28 g/mole and it behaves as an ideal gas. a. Calculate the force that the nitrogen gas exerts on the piston.

b. Calculate the volume of the gas if the temperature of the gas is 300 K.

c. In a certain process, the piston is allowed to move, and the gas expands at constant pressure and pushes the piston out 0.15 m. Calculate how much work is done by the gas.

d. Which of the following is true of the heat energy transferred to or from the gas, if any, in the process in part (c)? _______Heat is transferred to the gas. _______Heat is transferred from the gas. _______No heat is transferred in the process. Justify your answer.



33

41. 2009B4. The cylinder represented below contains 2.2 kg of water vapor initially at a volume of 2.0 m3

and an absolute pressure of 3.0x105 Pa. This state is represented by point A in the PV diagram below. The

molar mass of water is 18 g, and the water vapor can be treated as an ideal gas. a. Calculate the temperature of the water vapor at point A.

The absolute pressure of the water vapor is increased at constant

volume to 4.0x105 Pa at point B, and then the volume of the water

vapor is increased at constant pressure to 2.5 m3 at point C, as

shown in the PV diagram. a. Calculate the temperature of the water vapor at point C.

b. Does the internal energy of the water vapor for the process A→B→C increase, decrease, or remain the

same?

____Increase ____Decrease ____Remain the same

Justify your answer.

c. Calculate the work done on the water vapor for the process A→B→C



34

12. 2006Bform b #5.

A sample of ideal gas is taken through steps I, II, and III in a closed cycle, as shown on the pressure P versus volume V diagram above, so that the gas returns to its original state. The steps in the cycle are as follows.

I. An isothermal expansion occurs from point A to point B, and the volume of the gas doubles. II. An isobaric compression occurs from point B to point C, and the gas returns to its original volume. III. A constant volume addition of heat occurs from point C to point A and the gas returns to its original pressure.

(a) Determine numerical values for the following ratios, justifying your answers in the spaces next to each ratio.

i. B

A

P

P=

ii. C

A

P

P=

iii. B

A

T

T=

iv. C

A

T

T=

(b) During step I, the change in internal energy is zero. Explain why.

(c) During step III, the work done on the gas is zero. Explain why.



35

Video 6. 2nd Law of Thermodynamics 13. If you place a jar of perfume in the center of a room and remove the stopper, you will soon be able to smell

the perfume throughout the room. If you wait long enough, will all the perfume molecules ever be back in the jar at the same time? Why or why not?

14. Suppose you place an ice cube in a cup of room-temperature water and then seal them in a well-insulated

container. No energy can enter of leave the container. a. If you open the container an hour later, which do you expect to find: a cup of water, slightly cooler than

room temperature, or a large ice cube and some 100C steam?

b. Finding a large ice cube and some 100C steam would not violate the first law of thermodynamics. W =0 J

and Q = 0 J, because the container is sealed, and U = 0 J because the increase in thermal energy of the water molecules that have become steam is offset by the decrease in water molecules that have turned to ice. Energy is conserved, yet we never see a process like this. Why not?

15. Are each of the following processes reversible or irreversible? Would the second law of thermodynamics be

violated by any of the processes? Explain. a. A freshly baked pie cools on a window sill.

b. A neatly raked pile of leaves is scattered by the wind.

c. The wind gathers up the fallen leaves in a yard and leaves them in a neat pile. 16.


Answers to the AP Problems

36

42. 2008 B5 a) c. 0.005 m3

43. 2006 B5 a)i) 746 K ii) 559.5 K b) + 6250 K c) removed

44. 2007 B5 a) 1.26x104 N b) 0.0124 m3 c) 1885 J d) to gas

45. 2009B4 a) 592K b) 986 K c) increases because Temperature increases d) -200,000 J

46. 2006 form B 5 a) i) ½ ii) ½ iii) 1 iv) ½ b) isothermal so no

change in Temp means no change in internal energy c) isochoric, no change in volume means no work

is done

ap physics 2 unit 2: thermodynamics name: “we cannot … · zero hour in class homework ... extra...

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