Chapter 10 Temperature and Kinetic Theoryroselleachs.sharpschool.net/UserFiles/Servers/Server...Gas Laws, Absolute Temperature, and the Kelvin Temperature Scale Thermal Expansion The

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Chapter 10 Temperature and Kinetic

Theory

© 2010 Pearson Education, Inc.

Units of Chapter 10 Temperature and Heat

The Celsius and Fahrenheit Temperature Scales

Gas Laws, Absolute Temperature, and the Kelvin Temperature Scale

Thermal Expansion

The Kinetic Theory of Gases

Kinetic Theory, Diatomic Gases, and the Equipartition Theorem


10.1 Temperature and Heat

Temperature is a measure of relative hotness or coldness.

Heat is the net energy transferred from one object to another due to a temperature difference.

This energy may contribute to the total internal energy of the object, or it may do work, or both.


10.1 Temperature

and Heat


10.1 Temperature and Heat

A higher temperature does not necessarily mean that one object has more internal energy than another; the size of the object matters as well.

When heat is transferred from one object to another, they are said to be in thermal contact.

Two objects in thermal contact without heat transfer are in thermal equilibrium.


10.2 The Celsius and Fahrenheit Temperature Scales

A thermometer is used to measure temperature; it must take advantage of some property that depends on temperature. A common one is thermal expansion.


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10.2 The Celsius and Fahrenheit Temperature Scales

In everyday use, temperature is measured in the Fahrenheit or Celsius scale.

To convert from one to the other:


Which is the largest unit: one Celsius degree, one Kelvin degree, or one Fahrenheit degree?

a) one Celsius degree b) one Kelvin degree c) one Fahrenheit degree d) both one Celsius degree and

one Kelvin degree e) both one Fahrenheit degree

and one Celsius degree

Question 10.1 Degrees

It turns out that –40°C is the same temperature as –40°F. Is there a temperature at which the Kelvin and Celsius scales agree?

a) yes, at 0°C b) yes, at −273°C c) yes, at 0 K d) no

Question 10.2 Freezing Cold 10.3 Gas Laws, Absolute Temperature, and the Kelvin Temperature Scale

When the temperature of an ideal gas is held constant,

When the pressure is held constant,


10.3 Gas Laws, Absolute Temperature, and the Kelvin Temperature Scale

Combining gives the ideal gas law:

or

with Boltzmann’s constant:

N is the total number of molecules in the gas.



The ideal gas law can also be written

where n is the number of moles of gas and R is the universal gas constant:

A mole of a substance contains Avogadro’s number of molecules:


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A constant-volume gas thermometer is useful because the temperature is directly proportional to the pressure. If P-T curves are plotted for different gases, they converge at zero pressure.



The temperature at which this occurs is called absolute zero—no lower temperature is possible.

The Kelvin temperature scale has the same increments as the Celsius scale, but has its zero at absolute zero.



The three temperature scales are shown here. In physics calculations, the Kelvin temperature scale is used.

The Kelvin scale is also called the absolute scale, as the Kelvin temperature is proportional to the internal energy.


10.4 Thermal Expansion Most materials expand when heated. For small changes in temperature, the change in length is proportional to the change in temperature.


10.4 Thermal Expansion

The changes in area and in volume can be derived from the change in length.


10.4 Thermal Expansion


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Question 10.4 Glasses

a) run hot water over them both

b) put hot water in the inner one

c) run hot water over the outer one

d) run cold water over them both

e) break the glasses

Two drinking glasses are stuck, one inside the other. How would you get them unstuck?

a) gets larger

b) gets smaller

c) stays the same

d) vanishes

Metals such as brass expand when heated. The thin brass plate in the movie has a circular hole in its center. When the plate is heated, what will happen to the hole?

Question 10.5b Steel Expansion II

10.4 Thermal Expansion Water behaves nonlinearly near its freezing point—it actually expands as it cools. This is why ice floats, and why frozen containers may burst.


10.5 Kinetic Theory of Gases According to the kinetic theory of gases, pressure is due to elastic collisions of molecules with container walls.


10.5 Kinetic Theory of Gases Using the kinetic theory, it can be shown that

The mass and speed are those of an individual molecule.

The molecular kinetic energy can be related to the temperature:


10.5 Kinetic Theory of Gases

The internal energy of a monatomic gas is due to the kinetic energy of its atoms, and is therefore related to its temperature.


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Which has more molecules—a mole of nitrogen (N2) gas or a mole of oxygen (O2) gas?

a) oxygen b) nitrogen c) both the same

Question 10.8a Nitrogen and Oxygen I

Which weighs more—a mole of nitrogen (N2) gas or a mole of oxygen (O2) gas?

a) oxygen b) nitrogen c) both the same

Question 10.8b Nitrogen and Oxygen II

10.5 Kinetic Theory of Gases

The kinetic theory of gases also helps us understand diffusion as a result of the motion of molecules.


10.6 Kinetic Theory, Diatomic Gases, and the Equipartition Theorem

The atoms in a monatomic gas have only translational equilibrium to contribute to the internal energy. A diatomic molecule can also rotate around two distinct axes (x and y).



The equipartition theorem tells us what the contribution of the rotational states is to the internal energy.

A diatomic molecule has 5 degrees of freedom—translation in x, y, or z, rotation around x, and rotation around y.



The predicted internal energy of a diatomic gas is then:


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Boyle’s Law Boyle’s Law states that •  The pressure of a gas

is inversely related to its volume when T and n are constant.

•  If the pressure increases, volume decreases.

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In Boyle’s Law •  The product P x V is constant as long as T and n do

not change. P1V1 = 8.0 atm x 2.0 L = 16 atm L P2V2 = 4.0 atm x 4.0 L = 16 atm L P3V3 = 2.0 atm x 8.0 L = 16 atm L

•  Boyle’s Law can be stated as P1V1 = P2V2 (T, n constant)

PV Constant in Boyle’s Law

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Solving for a Gas Law Factor

The equation for Boyle’s Law can be rearranged to solve for any factor.

P1V1 = P2V2 Boyle’s Law To solve for V2 , divide both sides by P2.

P1V1 = P2V2 P2 P2

V1 x P1 = V2 P2

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Freon-12, CCl2F2, is used in refrigeration systems. What is the new volume (L) of a 8.0 L sample of Freon gas initially at 550 mm Hg after its pressure is changed to 2200 mm Hg at constant T?

STEP 1 Set up a data table Conditions 1 Conditions 2 P1 = 550 mm Hg P2 = 2200 mm Hg V1 = 8.0 L V2 =

Calculation with Boyle’s Law

?

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STEP 2 Solve Boyle’s Law for V2. When pressure increases, volume decreases. P1V1 = P2V2

V2 = V1 x P1 P2 V2 = 8.0 L x 550 mm Hg = 2.0 L 2200 mm Hg pressure ratio decreases volume

Calculation with Boyle’s Law (Continued)

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Learning Check For a cylinder containing helium gas indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant): 1) Pressure decreases 2) Pressure increases

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Solution For a cylinder containing helium gas indicate if cylinder A or cylinder B represents the new volume for the following changes (n and T are constant): 1) Pressure decreases B 2) Pressure increases A

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Charles’ Law In Charles’ Law •  The Kelvin temperature

of a gas is directly related to the volume.

•  P and n are constant.

•  When the temperature of a gas increases, its volume increases.

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•  For two conditions, Charles’ Law is written V1 = V2

(P and n constant)

T1 T2

•  Rearranging Charles’ Law to solve for V2

V2 = V1 x T2

T1

Charles’ Law: V and T

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Learning Check

Solve Charles’ Law expression for T2. V1 = V2 T1 T2

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Solution

V1 = V2 T1 T2 Cross multiply to give V1T2 = V2T1 Isolate T2 by dividing through by V1 V1T2 = V2T1 V1 V1 T2 = T1 x V2 V1

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•  The relationship between the four properties (P, V, n, and T) of gases can be written equal to a constant R. PV = R nT

•  Rearranging this expression gives the expression called the ideal gas law. PV = nRT

Ideal Gas Law

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The universal gas constant, R •  Can be calculated using the molar volume of a gas at STP. •  Calculated at STP uses 273 K,1.00 atm, 1 mole of a gas, and a

molar volume of 22.4 L. P V R = PV = (1.00 atm)(22.4 L) nT (1 mole) (273K) n T = 0.0821 L atm mole K

Universal Gas Constant, R

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Another value for the universal gas constant is obtained

using mm Hg for the STP pressure. What is the value

of R when a pressure of 760 mm Hg is placed in the R

value expression?

Learning Check

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What is the value of R when a pressure of 760 mm Hg is placed in the R value expression?

R = PV = (760 mm Hg) (22.4 L) nT (1 mole) (273 K) = 62.4 L mm Hg

mole K

Solution Question 10.9a Ideal Gas Law I

a) cylinder A

b) cylinder B

c) both the same

d) it depends on temperature T

Two identical cylinders at the same

temperature contain the same gas. If

A contains three times as much gas

as B, which cylinder has the higher

pressure?

Question 10.9b Ideal Gas Law II

a) cylinder A

b) cylinder B

c) both the same

d) it depends on the pressure P

Two identical cylinders at the same pressure contain the same gas. If A contains three times as much gas as B, which cylinder has the higher temperature?

Question 10.9c Ideal Gas Law III Two cylinders at the same temperature contain the same gas. If B has twice the volume and half the number of moles as A, how does the pressure in B compare with the pressure in A?

a) PB = ½ PA

b) PB = 2 PA

c) PB = ¼ PA

d) PB = 4 PA

e) PB = PA

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Chapter 10 Temperature and Kinetic Theoryroselleachs.sharpschool.net/UserFiles/Servers/Server...Gas Laws, Absolute Temperature, and the Kelvin Temperature Scale Thermal Expansion The