Thermal Physics Temperature and Thermal Equilibrium Kinetic Theory - - PDF document

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Thermal Physics

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Topics to be covered

Temperature and Thermal Equilibrium Kinetic Theory Gas Laws Internal Energy Heat Work Laws of Thermodynamics Heat Engines

Slide 3 / 105 Thermodynamics System

Originally, in 1824 Sadi Carnot describe a thermodynamics system as the working substance under study. In Thermodynamics - system is any region completely enclosed within a well defined

• boundary. Everything outside the system is

then defined as surroundings. Very often in this chapter we will use a word "system" instead of cylinder of gas, container filled with water, ice cube.

Slide 4 / 105 Temperature

The concept of temperature is rooted in qualitative ideas of "hot" and "cold" based on our sense of

• touch. An object that feels hot has a higher

temperature than a similar object that feels cold. Measuring temperature based on our sense is very subjective. When we touch different objects in our classroom we will find that metallic objects feel cooler than wooden or plastic objects which is not true because they have all been in the same room for a long time. They all have the same temperature.

Slide 5 / 105 Temperature

There is a better way of measuring temperature based on properties of matter that depend on

• temperature. The volume of liquid, length of a

metal rod, gas pressure, electroconductivity, and the color of a hot glowing object.

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Thermometers are instruments designed to measure temperature.

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Slide 7 / 105 Temperature

In everyday life, we use liquid-in-tube thermometers which are based on thermal expansion of liquids. In addition to thermometers we need some kind of a common scale that we can use to present different temperatures. In Europe, the most common is Celsius scale. In the United State, the most common is Fahrenheit scale. In science, the most important is Absolute or Kelvin scale.

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The relationships among three different temperature scale are presented by the table below.

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The following formulas we can use to convert temperature from one scale to another.

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1 Which temperature scale never gives negative temperatures?

A

Fahrenheit

B

Kelvin

C

Celsius

D

Reaumur

E

All of the above

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2 Freezing point of water is 32 ̊F; what is this on Celsius scale? A 32 B C 273 D 212 E 25

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3 “Room temperature” is often taken to be 68 ̊F; what is this

• n the Celsius scale?

A 25 B 45 C 34 D 20 E 15

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4 The temperature of a human body is 37 ̊C; what is this on the Fahrenheit scale? A 25.9 B 60.5 C 78.2 D 98.6 E 42.8

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5 The temperature of boiling water is 100 ̊C; what is this on the Fahrenheit scale? A B 32 C 100 D 273 E 212

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6 Melting point of ice is 0 ̊C; what is this on the Kelvin scale? A B 32 C 373 D 273 E 212

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7 Absolute zero is what temperature on the Celsius scale? A B 273 C

• 32

D

• 273

E 32

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Thermal Equilibrium and the Zeroth Law

• f Thermodynamics

Two objects placed in thermal contact will eventually come to the same temperature. When they do, we say they are in thermal equilibrium. The zeroth law of thermodynamics says that if two

• bjects are each in equilibrium with a third object, they

are also in thermal equilibrium with each other.

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8 Three objects A, B, and C initially have different temperatures TA>TB>TC. Objects A and B are separated by an insulating plate but they are in contact with object C through a conducting

• platform. Which of the following is true when
• bjects A and B reach thermal equilibrium with
• bject C?

A The temperature of all three objects stays unchanged B Object A has higher temperature than object B and C C Object C has higher temperature that object A and B D Object B has higher temperature that object A and C E All three objects have the same temperature

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9 A simple pendulum is made of a steel string supporting a brass

• sphere. The temprerature in a room with the pendulum is increased

from 15 C to 30 C. Which of the folowing is true about the period of

• scillations?

A

The period is doubled

B

The period stays unchanged

C

The period is increased by #2

D

The period is decreased by #2

E

The period is slightly increased

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Thermal Expansion

Volume thermal expansion occurs when increasing temperature causes increases in volume for both solid and liquid materials. Where # is the coefficient of volume expansion.

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10

A glass flask is filled with glycerin up to the top. When the temperature of surroundings is increased by a few degrees, which

• f the following is true about the level of glycerin in the flask? (The

coefficients of volume expansion are:#glycerin=49x10-5 K-1, #glass= 2x10-5 K-1) A The level of glycerin in the flask goes down B The level of glycerin stays unchanged because the both expand C Glycerin spills out of the flask D It can't be determined from the given information

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Thermal Expansion

Water, in the temperature range from 0 oC to 4 oC, decreases in its volume and increases in density. Above 4oC, water expands when

• heated. Hence water has its greatest density at 4 oC. Water also

expands when it freezes, which is why a piece of ice floats on water surface.

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Kinetic Theory

Many properties of matter such as: thermal expansion, melting, boiling, cooling, heating... can be explained based

• n the concept that matter is made up of tiny particles.

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The idea that all familiar matter is made up of atoms goes back to the ancient Greeks. According to them if we were cut a piece of iron into smaller and smaller portions, eventually a smallest piece of iron would be obtained which could not be divided further. This smallest piece is called an atom (indivisible).

Kinetic Theory

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Kinetic Theory

Kinetic Theory studies the macroscopic properties of matter in terms of its atomic structure and behavior. This theory has a tremendous practical importance; once we have this understanding , we can design materials with specific desired properties. The analysis to this theory has led to development of high- strength steels, glasses with special optical properties, semiconductors.

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Kinetic Theory

The study of a real gas is very complicated from mathematical point of view. In our discussion of the kinetic theory we will be using a simplified mathematical model which is called - ideal gas.

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Kinetic Theory

The assumptions of ideal gas model are:

• 1. A container contains a very large number of particles

(atoms, molecules).

• 2. The atoms behave as point particles; their size is

small in comparison to the average distance between particles and to the size of the container.

• 3. The particles are in constant motion; they obey

Newton's Laws of motion. Each particle collides

• ccasionally with a wall of the container. These

collisions are perfectly elastic.

• 4. The walls of the container are rigid and very massive.

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11 Which of the following is not included into the assumptions of the ideal gas?

A

The number of molecules in a container is very large

B

The molecules interact when they collide with each other

C

The molecules interact all the time during their motion because

• f intermolecular forces

D

The collisions between molecules are perfectly elastic

E

The size of molecules can be ignored

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Kinetic Theory

Now we will calculate the pressure in the ideal gas based on kinetic theory. First we will find the change in momentum during one single collision of a molecule with a wall of the container. The change in momentum in the direction perpendicular to the wall is: Assuming that the collision is perfectly elastic and

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Kinetic Theory

If a molecule is going to collide with a given wall area A during a small time interval #t, which is the time it takes the molecule to travel across the box and back again, a distance equal to 2L. Where 2L = vx#t.

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The time between the collisions is very small, so the number of collisions per second is very large. According to Newton's Laws the average force will be equal to the force exerted during one collision divided by the time between the collisions.

Kinetic Theory

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Kinetic Theory

To calculate the force due to all the molecules in the box, we have to add the contributions of each. The average value of the square of the x component

• f velocity is

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Kinetic Theory

The force due to all molecules is From Pythegorian Theorem: Since all molecules move in random directions and there is no preference between x, y, and z we can write the following:

• r

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Kinetic Theory

Now we can change the square of the velocity component to the square of the velocity. The pressure on the wall is force per unit of area.

• r

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Kinetic Theory

The last equation can be modified by replacing average velocity with the average kinetic energy

• f molecules.

It was found from the series of experiments that which is called the ideal-gas equation. Where k= 1.38x10-23 J/K is Boltzmann's constant.

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Kinetic Theory

After comparing two last equations we can conclude: The average kinetic energy of molecules in a gas is directly proportional to the absolute

• temperature. This is the most important result of

kinetic theory. The higher the temperature, the faster molecules move on the average.

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Kinetic Theory

When we analyze two equations: and We can find the root-mean-square velocity or vrms

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Kinetic Theory

Summary to the Kinetic Theory:

• 1. The pressure in the ideal gas is directly

proportional to the average square of the velocity

• f molecules.

The faster the molecules move the more frequent they collide with the walls and greater change in the momentum during the collisions.

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Kinetic Theory

Summary to the Kinetic Theory:

• 2. The first time in the history of physics the

temperature was explained on the microscopic level not based on human sense. According to the kinetic theory, the temperature can't be negative and it reaches zero (absolute zero) when the average translational kinetic energy of molecules is zero.

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Kinetic Theory

Summary to the Kinetic Theory:

• 3. The average velocity of molecules depends on

absolute temperature and molecular mass. The increasing temperature causes molecules to move faster and light molecules move faster then heavy ones.

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12 If the average kinetic energy of molecules is increased while the number of moles is kept constant, what happens to the pressure of an ideal gas?

A

It increases

B

It decreased

C

It remains constant

D

It decreases and then increases

E

None from the above

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13 The average kinetic energy of molecules can be increased by increasing which of the following?

A

Pressure

B

Volume

C

Temperature

D

Number of moles

E

All of the above

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14 If the temperature of an ideal gas is increased from 25 C to 50 C, what happens to the average kinetic energy of the molecules?

A

It doubles

B

It quadruples

C

It is cut to one-half

D

It is cut to one-fourth

E

It slightly increases

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15 If the absolute temperature of an ideal gas is doubled, what happens to the average speed of the molecules?

A

It doubles

B

It quadrupes

C

It increases by #2

D

It decreases by #2

E

It remains unchanged

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Kinetic Theory

Kinetic Theory, like other theories in physics, requires an experimental proof. Historically, the experiments with gasses were performed long time before the completion of the kinetic theory. In the next section of the chapter, we will discuss the Gas Laws that were discovered by different scientists.

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Gas Laws

Boyle's Law-the pressure in a gas is inversely proportional to its volume when the temperature is kept

• constant. This process is called "Isothermal".

constant

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16 Which of the following graphs represents the isothermal process?

A B C D E

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17 A container with an ideal gas at pressure P is compressed to one- fourth of its volume while the temperature is kept constant. What is the new pressure in the gas in terms of P?

A

2P

B

4P

C

P

D

1/2P

E

1/4P

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Gas Laws

Charles's Law- the volume of a given amount of gas is directly proportional to the absolute temperature when the pressure is kept constant. This process is called "Isobaric".

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18 Which of the following graphs represents the isobaric process?

A B C D E

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19 An ideal gas is taken from one state at the temperature T1=273 K to another state at the temperature T2 =546 K isobarically. What happens to the volume of the ideal gas?

A

It quadruples

B

It is cut to one-fourth

C

It doubles

D

It is cut to a half

E

It doesn't change during the isobaric process

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Gas Laws

Gay-Lussac's Law- the pressure of a gas is directly proportional to the absolute temperature, when the volume stays unchanged. This process is called "Isochoric".

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20 Which of the following graphs represents the isochoric process?

A B C D E

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21 A sample of an ideal gas is enclosed into a container with rigid

• walls. The temperature of the gas is changed from 20 oC to 60 oC.

What happens to the pressure in the gas?

A

It doubles

B

It quadruples

C

It triples

D

It is cut to one-third

E

It is slightly increased

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Gas Laws

Gas Laws can be combined into a single more general relationship between the pressure, volume, and temperature a fixed quantity of gas. This equation is called the Ideal Gas Law. Where n is the number of moles and R is the universal gas constant.

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22 The number of moles of an ideal gas is doubled while the temperature and volume remain the same. What happens to the pressure in the gas?

A

It doubles

B

It quadruples

C

It remains the same

D

It is decreased to one-half

E

It is decreased to one-fourth

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23 An ideal gas is taken through a closed cycle A⇒B⇒C⇒A. As shown

• n the diagram. Which point is associated with the highest

temperature?

A

A

B

B

C

C

D

All points are related to the same temperature

E

More information is required

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Internal Energy

Similar to mechanics when we use two different approaches - dynamics and energy to explain the same processes, can be done in thermal physics. In the previous section, we spend time to explain thermal processes by using three parameters: pressure, volume, and temperature. In the following section we will be using more elegant - energy approach to explain the same thermal processes.

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Internal Energy

When a pendulum is set to oscillations over a long period of time we can observe that its amplitude decreases to zero. It seems like mechanical energy disappeared, which is not true because the temperature of the pendulum and surroundings has

• changed. The mechanical energy is transformed into

the kinetic energy of molecules.

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Internal Energy

The internal energy of an ideal gas depends on temperature and the number of moles of gas. An increase in temperature causes an increase in internal energy.

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24 The temperature of a monatomic ideal gas is increased from 35 oC to 70 oC. How does it change its internal energy?

A

It doubles

B

It quadruples

C

It is slightly increased

D

It is decreased to one-half

E

It is decreased to one-fourth

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25 The state of an ideal gas is changed through the closed path 1⇒ 2⇒ 3⇒ 1. What happens to the internal energy of the gas between point 2 and point 3?

A

It increases

B

It decreases

C

It remains constant

D

It decreases and then increases

E

It increases and then decreases

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The internal energy of a thermodynamic system can be changed in two different ways: adding heat to the system or doing work on the system.

Internal Energy

The state of any thermodynamic system can be described with the internal energy.

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Heat

We introduced the concept of internal energy now it is time to explain the concept of heat. Heat is a transfer of energy from one object to another because of difference in temperature. Where m - mass, #T - change in temperature, and c - specific heat. Specific heat is a quantity characteristic of the material.

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26 The mechanical equivalent of heat was measured by

A

Kelvin

B

Boltzmann

C

Boyle

D

Joule

E

Charles

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27 The amount of heat required to raise the temperature of 1 kg of a substance by 1 oC is referred to which of the following?

A

Latent heat of vaporization

B

Latent heat of fusion

C

Specific heat

D

Calorie

E

Joule

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28 The ocean temperature doesn't change drastically because of

A

Water is a good heat conductor

B

Wather is a good heat radiator

C

Water has a very high specific heat

D

Water has a very low melting temperature

E

Water has a very high boiling point

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Heat

When a system changes its phase from solid to liquid a certain amount of energy is involved. LF is the heat of fusion. The energy required to change a substance from the liquid to the vapor can be presented by the following formula. LV is the heat of vaporization.

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29 When a solid metal melts its temperature

A

Increases

B

Decreases

C

Remains constant

D

Increases and then decreases

E

Decreases and then increases

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30 Which of the following is true about melting process?

A

The energy is required to increase the average kinetic energy of molecules

B

The energy is required to decrease the average kinetic energy of molecules

C

The energy is required to increase the potential energy between the molecules

D

The energy is required to decrease the potential energy between the molecules

E

No energy is required for this process it happens spontaneously

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31 When water vapor condenses

A

The temperature increases

B

The temperature decreases

C

The energy is absorbed

D

The energy is released

E

None from the above

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Heat

Heat can be transfered from one object to another in three different ways: conduction, convection, and radiation. Conduction is a transfer of heat as a result of molecular collisions.

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Conduction is a transfer of heat as a result of molecular collisions. k- constant, is called the thermal conductivity, which is characteristic of the material.

Conduction

is the rate of heat transfer.

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32 When we double the thickness of a wall with the same material, the rate of heat loss due to the same temperature difference across the thickness is

A

Doubled

B

Quadrupled

C

Unchanged

D

Cut to one-half

E

Cut to one-fourth

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Convection

Convection is the process where heat is transfered by the mass movement of molecules from one place to anoter. Convection in gasses Convection in liquids

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33 Convection can occur

A

Only in solids

B

Only in liquids

C

Only in gasses

D

Only in liquids and gasses

E

In solids, liquids, and gasses

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34 Which of the following is responsible for raising the temperature of water in a pot placed on a hot stove?

A

Conduction

B

Convection

C

Radiation

D

Vaporization

E

Condensation

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Radiation

Energy transfer by electromagnetic waves. Stefan-Boltzmann equation. The rate at which an object radiates energy is proportional to the fourth power of the absolute temperature. e - emissivity, is a number between 0 and 1 that depends on the material.

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35 When the temperature of a heater is doubled, by what factor does the radiating power change?

A

2

B

4

C

8

D

16

E

32

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Work in Thermodynamics

A simple and very common example of a thermodaymic system is a quantity of gas enclosed in a cylinder with a movable piston.

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Work in Thermodynamics

First we consider the work done by the gas during its expansion. An expanding gas always dose positive work. Suppose that the cylinder has a cross-sectional area A and the pressure exerted by the gas is Pgas. The total force exerted by the gas on the piston is F = pA. When the piston moves up a distance #x and the pressure P is constant, the work W is

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Work in Thermodynamics

When the piston moves down, so the volume of the gas decreases, then the work done by the gas is negative. During the compression of the gas in the cylinder the work done by the external force Fext is positive. The relationship between work done by the gas and work done on the gas can be presented by following:

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Work in Thermodynamics

This relationship can be represented as a graph of p as a function of V on a pV - diagram. The work done equals the area under the curve on a pV-diagram. In an expansion, the work done by the gas is positive.

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Work in Thermodynamics

In a compression, the work done by the gas is negative.

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36 The state of an ideal gas is changed in a closed path 1⇒2⇒3⇒1. Which of the following is true about work done by the gas between point 1 and point 2?

A

Work done by the gas is positive

B

Work done by the gas is negative

C

Work done by the gas is zero

D

Work done by the gas is greater than work done on the gas

E

Work done by the gas is less than work done on the gas

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37 The state of an ideal gas is changed in a closed path 1⇒2⇒3⇒1. Which of the following is true about work done by the gas between point 2 and point 3?

A

Work done by the gas is positive

B

Work done by the gas is negative

C

Work done by the gas is zero

D

Work done by the gas is greater than work done on the gas

E

Work done by the gas is less than work done on the gas

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First Law of Thermodynamics

In previous sections of this chapter we defined the internal energy, heat, and work in thermodynamics. Now we will combine them in one formula- conservation of energy in thermal processes.

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First Law of Thermodynamics

where Q is the net heat added to the system, W' is the net work done on the system, and #U is the change in internal energy. First Law of Thermodynamics

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38 150 J of heat is added to a system and 100 J of work done on the

• system. What is the change in the internal energy of the system?

A

250 J

B

150 J

C

100 J

D

50 J

E

0 J

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39 250 J of heat is added to a system and the system does 100 J of work on surroundings. What is the change in the internal energy of the system?

A

250 J

B

150 J

C

100 J

D

50 J

E

0 J

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First Law of Thermodynamics

Isothermal process is one where temperature stays

• unchanged. When T = constant⇒#T = 0.

The internal energy of an ideal gas depends on temperature and for this process #U = 0 Since the change in internal energy is zero the First Law of Thermodynamics: The heat added to the gas in an isothermal process equals the work done by the gas.

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First Law of Thermodynamics

Adiabatic process is one in which no heat flows into or out of the system. When heat is zero then the first law of thermodynamics: The net work done on the gas equals the change in internal energy.

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First Law of Thermodynamics

Isochoric process is one where volume stays unchanged. When #V = 0 ⇒W' = 0 The first law of thermodynamics is The net heat added to the system equals the change is internal energy.

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40 A sample of an ideal gas is taken through a closed cycle. Which of the following is true about the change in internal energy and work done on the gas between point 2 and point 3?

A

#U =0, W' > 0

B

#U =0, W' = 0

C

#U =0, W' < 0

D

#U > 0, W' > 0

E

#U < 0, W' < 0

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Second Law of Thermodynamics

Many thermal processes proceed naturally in one direction but not the opposite. For example, heat by itself always flows from a hot object to a cooler object, never the reverse. The reverse process would not violate the first law of thermodynamics; energy would be conserved. In order to fix this problem with reversible processes, scientists formulated a new principle-the second law of thermodynamics.

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Second Law of Thermodynamics

Heat flows naturally from a hot object to a cold

• bject; heat never flows spontaneously from a

cold object to a hot object.

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Heat Engines

The basic idea behind of any heat engine is that mechanical energy can be obtained from thermal energy. Denis Papin first time in history of physics described three basics components of any heat engine: high-temperature reservoir, low-temperature reservoir, and engine containing gas or steem.

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The high-temperature reservoir transfers an amount of heat QH to the engine, where part of it is transformed into work W (during the expansion of gas) and the rest, QL, is exhausted to the low- temperature reservoir.

Heat Engines

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Heat Engines

The efficiency e of any heat engine can be defined as a ratio

• f work W to the heat input QH.

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Heat Engines

The question of increasing the efficiency

• f a heat engine was very difficult in
• physics. This question was answered in

1824 by the French engineer Sadi Carnot. Sadi Carnot developed a hypotetical, idealized heat engine that has the maximum possible efficiency consistent with the second law of thermodynamics.

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Heat Engines

The Carnot engine consists of two reversible isothermal processes A⇒B, C⇒D, and two reversible adiabatic processes B⇒C, D⇒A. The Carnot engine operates between two temperature TH and TL.

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Heat Engines

Carnot Theorem- no engine can have more efficiency than a Carnot engine operating between the same two temperatures. Carnot ideal efficiency

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Second Law of Thermodynamics and Entropy

The total entropy of an isolated system never decreases (Second Law of Thermodynamics). The change in entropy S of a system, when heat Q is added to it by a reversible process at a constant temperature T. Entropy is a measure of the disorder of a system. For any real process, the change in entropy is greater than zero:#S>0.