AP Physics Chapter 12 Study Guide
Thermal Properties of Matter

The Atomic Model of Matter

Three Phases of Matter

Gas – A gas is a state of matter, consisting of a collection of particles (molecules, atoms, ions, electrons, etc.) without a definite shape or volume that are in more or less random motion.

gas

Liquid – A liquid is a fluid that has the particles loose and can freely form a distinct surface at the boundaries of its bulk material.

liquid

Solid – A solid object is in the states of matter characterized by resistance to deformation and changes of volume.

solid

 

Atomic Mass Number (A) – the sum of the number of protons and neutrons.

Atomic Mass – the mass of an atom of a chemical element expressed in atomic mass units

atomic mass unit

 

Molecular Mass – the sum of the atomic masses of the atoms forming the molecule.

Mole – The mole is defined as the amount of substance of a system which contains as many "elemental entities" (e.g., atoms, molecules, ions, electrons) as there are atoms in 12 g of carbon-12.

Avegadro's Number symbolavegadro

 

moles

Moles of a substance in terms of the number of basic particles.

 

mass

Moles of a substance in terms of its mass.

 

Thermal Expansion

expansionexpansion

 

volume expansion

Volume thermal expansion

volume

linear expansion

Linear thermal expansion

linear

area

 

Example 1

When rod 1 is heated by an amount delta, its length increases by delta. If rod 2, which is twice as long as rod 1 and made of the same material, is heated by the same amount, does its length increase by (a)delta, (b) delta, or (c)delta?

 

 

 

Example 2

The Eiffel Tower, constructed in 1889 by Alexandre Eiffel, is an impressive latticework structure made of iron. If the tower is 301 m high on a 22°C day, how much does its height decrease when the temperature cools to 0.0°C?

 

 

 

 

Example 3

A washer has a hole in the middle. As the washer is heated, does the hole (a) expand, (b) shrink, or (c) stay the same?

 

 

Example 4

A copper flask with a volume of example is filled to the brim with olive oil. If the temperature of the system is increased from 6.0°C to 31°C, how much oil spills from the flask? (example)

 

 

 

 

 

 

Pressure and the Kinetic Theory of an Ideal Gas

Temperature

ideal gas

 

temperature

 

Pressure

pressure

 

pressure

Definition of pressure in a gas as the force-to-area ratio.

pascal

 

Measuring Pressure

1 standard atmosphere = 1 atm = 101300 Pa = 101.3 kPa

1 atm = 14.7 psi

 

Gauge pressure – Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.

gauge pressure

 

 

Ideal-Gas Law

ideal gas

 

ideal gas law

ideal gas law

 

gas constant

 

 

Example 5

A person's lungs might hold 6.0 L of air at body temperature (310 K) and atmospheric pressure (101 kPa). Given that the air is 21% oxygen, find the number of oxygen molecules in the lungs.

 

 

 

 

 

 

Example 6

Feeling a bit cool, you turn up the thermostat in your house or apartment. A short time later the air is warmer. Assuming the room is well sealed, is the pressure of the air (a) greater than, (b) less than, or (c) the same as before you turned up the heat?

 

 

Example 7

A cylindrical flask of cross-sectional area A is fitted with an airtight piston that is free to slide up and down. Contained within the flask is an ideal gas. Initially the pressure applied by the piston is 130 kPa and the height of the piston above the base of the flask is 25 cm. When additional mass is added to the piston, the pressure increases to 170 kPa. Assuming the system is always at the temperature 290 K, find the new height of the piston.

 

 

 

 

 

Example 8

Consider again the system in the previous example. In this case the temperature is changed from an initial value of 290 K to a final value of 330 K. The pressure exerted on the gas remains constant at 130 kPa, and the initial height of the piston is 25 cm. Find the final height of the piston.

 

 

 

 

 

 

Example 9

A cylinder contains 12 L of oxygen at 20°C and 15 atm. The temperature is raised to 35°C, and the volume is reduced to 8.5 L. What is the final pressure of the gas in atmospheres? Assume that the gas is ideal.

 

 

 

 

 

 

Ideal-Gas Processes

Properties

1. The quantity of gas is fixed.

2. There is a well-defined initial state.

3. There is a well-defined final state.

 

process

 

pV Diagrams

 

pV diagram

pV diagram

 

Constant-Volume Processes (isovolumic)

A constant-volume process appears on a pV diagram as a vertical line.

constant volume constant volume

 

Constant-Pressure Processes (isobaric)

A constant-pressure process appears on a pV diagram as a horizontal line.

constant pressure constant pressure

 

 

Constant-Temperature Process (isothermal)

A constant-temperature process appears on a pV diagram as a hyperbola.

constant temperature constant temperature

constant temperature

 

Adiabatic Processes

A process in which no heat energy is transferred between the gas and the environment. (Q = 0)

adiabatic process

 

Work

work

work

 

work

 

A few things about work and pV diagrams

1. In order for a gas to do work, the volume must change. Thus no work is done in a constant-volume process.

2. The work done by a gas work is positive when the gas expands, but negative when the gas is compressed.

3. For any ideal-gas process, you must use the geometry of the pV diagram to calculate the area under the graph.

4. To calculate work, pressure must be in Pa and volume in meters.

5. First Law of Thermodynamics (work)

work

 

Example 10

A gas with a constant pressure of 150 kPa expands from a volume of example to a volume of example. How much work does the gas do?

 

 

 

 

 

 

Example 11

A gas expands from an initial volume of example to a final volume of example as the pressure increases linearly from 110 kPa to 230 kPa. Find the work done by the gas.

 

 

 

 

 

 

 

 

Example 12

A cylinder holds 0.50 mol of a monatomic ideal gas at a temperature of 310 K. As the gas expands isothermally from an initial volume of example to a final volume of example, determine the amount of heat that must be added to the gas to maintain a constant temperature.

 

 

 

 

 

 

 

 

 

Example 13

When a certain gas is compressed adiabatically, the amount of work done on it is 640 J. Find the change in internal energy of the gas.

 

 

 

 

 

 

 

 

Specific Heat and Heat of Transformation

Specific Heat (c) – the heat required to raise the temperature of one kilogram of a substance one degree kelvin.

specific heat

Heat needed to produce a temperture change temperature for mass M with specific heat c.

 

Example 14

The heat capacity of 1.00 kg of water is 4186 J/K. What is the temperature change of the water if (a) 505 J of heat is added to the system, or (b) 1010 J of heat is removed?

 

 

 

 

 

 

Phase Changes

melting melting

 

phase diagram

Phase Diagram

 

Heat of Transformation

heat of transformation

Heat of fusion fusion

Heat of vaporization vaporization

 

Heat Engines

heat engine

 

Carnot Cycle

heat

An isothermal expansion during which an amount of heat enters the system going from A to C.

fig

An isothermal compression back to A where heat is ejected from the system.

 

Heat Engine:

A heat engine is a cyclic device that converts thermal energy into work-out.

Examples of heat engines are the gasoline and the diesel engines.

fig

Gasoline engine

fig

Diesel engine

 

 

The Carnot Cycle is a four-stage reversible sequence:

1. isothermal expansion (from A to B) with the reception of heat in (hot) at a constant high temperature

2. adiabatic expansion (from B to C)

3. isothermal compression (from C to D) with the rejection of heat out (cold) at a low temperature

4. adiabatic compression (from D to A).

 

fig

Carnot Cycle

fig

Carnot Cycle