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.
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.
Solid – A solid object is in the states of matter characterized by resistance to deformation and changes of volume.
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
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 –
Moles of a substance in terms of the number of basic particles.
Moles of a substance in terms of its mass.
Volume thermal expansion
Linear thermal expansion
When rod 1 is heated by an amount , its length increases by . 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), (b) , or (c)?
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?
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?
A copper flask with a volume of 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? ()
Pressure and the Kinetic Theory of an Ideal Gas
Definition of pressure in a gas as the force-to-area ratio.
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.
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.
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?
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.
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.
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.
1. The quantity of gas is fixed.
2. There is a well-defined initial state.
3. There is a well-defined final state.
Constant-Volume Processes (isovolumic)
A constant-volume process appears on a pV diagram as a vertical line.
Constant-Pressure Processes (isobaric)
A constant-pressure process appears on a pV diagram as a horizontal line.
Constant-Temperature Process (isothermal)
A constant-temperature process appears on a pV diagram as a hyperbola.
A process in which no heat energy is transferred between the gas and the environment. (Q = 0)
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 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 .
5. First Law of Thermodynamics ()
A gas with a constant pressure of 150 kPa expands from a volume of to a volume of . How much work does the gas do?
A gas expands from an initial volume of to a final volume of as the pressure increases linearly from 110 kPa to 230 kPa. Find the work done by the gas.
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 to a final volume of , determine the amount of heat that must be added to the gas to maintain a constant temperature.
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.
Heat needed to produce a temperture change for mass M with specific heat c.
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?
Heat of Transformation
Heat of fusion
Heat of vaporization
An isothermal expansion during which an amount of heat enters the system going from A to C.
An isothermal compression back to A where heat is ejected from the system.
Examples of heat engines are the gasoline and the diesel engines.
The Carnot Cycle is a four-stage reversible sequence:
1. isothermal expansion (from A to B) with the reception of heat in () 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 () at a low temperature
4. adiabatic compression (from D to A).