AP Physics II.C

Kinetic Theory and Thermodynamics

The Ideal Gas Law

An ideal gas – one of low density (i.e. particles are far enough apart they have few interactions), low pressure (a little less than 1 atm.) and a temperature that is not near

the boiling point for that gas.

Three Relationships for Gasses

• Pressure and volume (Boyle’s Law)• Volume and temperature (Charles’ Law)• Pressure and temperature (Gay-Lussac’s

Laws)

So, an ideal gas is one that obeys this relationship between pressure,

volume and temperature. PV = nRT is known as the Ideal Gas Law. R is

the universal gas constant (8.315 J/mol·K), n is the number of moles and temperature is given in Kelvin.

Avagadro’s constant and moles (the gram equivalent of the

particle’s atomic or molecular mass)

• One mole of carbon-12 = ?• One mole of CO2 = ?• One mole of water = ?• One mole of oxygen = ?

Ex. A 0.10 mole sample of gas is confined to a jar whose volume if 4.0 L. What is the temperature of the gas if the pressure is 2.0 atm?

Pre-AP: Time out to talk about pressure

Ex. A cylindrical container of radius 15 cm and height 30 cm contains 0.6 mole of a gas at 433 K. How much force does the confined gas exert on the lid of the container?

14.3 Kinetic Theory of Gasses

The concept that gasses are composed of atoms in continuous

random motion is called the Kinetic Theory of Gasses.

So . . . What we’ve found is the average kinetic energy of gas

molecules is directly proportional to their absolute temperature

Ex. A tank contains two 2.0 mol of He gas at 20.0º C. Find theaverage kinetic energy per molecule and the average speed ofof the molecule.

Ex. By how much must the temperature of a sample of gas increase to triple the average speed of the molecules?

Internal Energy of a Monatomic Ideal Gas

Thermodynamics – the branch of physics which studies laws

relating heat and work

Closed system (mostly what we are concerned with) – one in

which no mass enters or leaves (but energy may be exchanged

with the environment)

State of the system – described by giving values for pressure,

volume, temperature and mass.

First Law of Thermodynamics

The internal energy of a system can change due to

• An addition or loss of heat (Q is positive if the system gains heat; Q is negative is the system loses heat)

• Work done on or by the system (work is positive if work is done on the system; work is negative if work is done by the system – this ain’t what your book says)

The First Law of Thermodynamics as an equation

(a statement of conservation of energy)

ΔU = Q + W

Ex. 2500 J of heat are added to a system and 1800 J of work is doneon the system. What is the change in internal energy? What is thechange in internal energy if 1800 J of work is done by the system?

Thermal Processes

The process occurs slowly enough that uniform pressure exists throughout all regions of the

system at all times.

1. Isobaric (constant pressure) – basically a way to derive a

formula

PV diagram for isobaric process (what is the area under the curve?)

2. Isothermal Process (constant temperature)

An expanding balloon

PV diagram for isothermal process

Calculating work for an isothermal process

An isothermal process and the First Law

3. Adiabatic – no heat flows in or out of the system (Q is

constant) Examples: bicycle pump, diesel engine, stretching a rubber band, compressed gas

released from a container

PV diagram

Calculating work – another non-boxer. Work is estimated from the area under the curve as it is for any

PV diagram.

An adiabatic process and the First Law

Note: two adiabatic processes are always connected by two isotherms (a Carnot engine –

more on this later)

4. Isovolumetric (isochoric) – constant volume

An isovolumetric process and the First Law

PV diagram for an isochoric process

The First Law and an Isochoric Process

Ex. What is the work done on/by the gas for each process shown in the PV diagram? Is work done on or by the gas in each process? What is the net work done for the cycle? Is the net work done on or by the gas?

Ex. A 0.5 mol sample of an ideal gas is brought from state a to state b when 7500 J of energy is added along the path shown in the PV diagram. Find a) the temperature at a b) the temperature at b c) the work done by the gas during the process ab and d) the change in internal energy of the gas.

Ex. A 0.5 mol sample of an ideal monatomic gas is brought from state a to state b along the path shown in the following PV diagram. a) What is the work done by the gas during these three process? b) What is the change in internal energy of the gas for these three processes? c) What is the net heat added during theses three processes?

Ex. A 0.5 mol sample of an ideal gas is brought from state a back to state a along the path shown in the following PV diagram. What is a) the change in internal energy for the cycle? b) the net work done on the gas during the cycle c) the heat removed during the cycle?

Three Parts of a Heat Engine (a device that uses heat to perform

work)• Hot reservoir (place from which the engine

receives heat)• Working substance (device on which the

input heat performs work)• Cold reservoir (remainder of input heat that

is rejected at a temperature lower than the input heat)

Ex. A heat engine draws 800 J of heat from the hot reservoir, and discards 450 J of heat to its cold reservoir during each cycle. How much work does this engine perform per cycle and what is its thermal efficiency?

A note on power

Carnot’s Principle and the Carnot Engine. A Carnot engine is an “ideal engine” that shows the

maximum efficiency at which a heat engine can operate between

two temperatures.

2nd Law of Thermodynamics (Kelvin-Plank statement) – no device is possible whose sole effect is to

transform a given amount of heat into work (no heat engine is 100%

efficient)

The Carnot efficiency and absolute zero

Ex. An engine manufacturer makes the following claims: the heatinput per second of the engine is 9.0 kJ at 325 K. The output persecond is 4.0 kJ at 225 K. Are the claims valid?

Concept Question Suppose a heat engine receives 1000 J of heatfrom a hot reservoir, delivers 1000 J of work and rejects no heatto the cold reservoir. Does this engine violate the 1st Law, 2nd Lawor both?

A note on entropy

Refrigerators, air conditioners and heat Pumps

Heat can flow from cold to hot if work is done on the gas.

Comparing a heat pump to a conventional heater

PV diagram for a heat engine

PV diagram for a heat pump

Ex. An ideal (Carnot) heat pump is used to heat a house to a temperature of 294 K. How much work is done by the pump to deliver 3350 J of heat into the house when the outdoor temperature is 273 K?