Thermodynamics Notes

Temperature, Heat, Kinetic Theory, and Thermodynamics
Objectives
Students should understand the “mechanical equivalent of heat” so they can determine how much heat
can be produced by the performance of a specified quantity of mechanical work.
Students should understand heat transfer and thermal expansion, so they can:
o Calculate how the flow of heat through a slab of material is affected by changes in the thickness or
area of the slab, or the temperature difference between the two faces of the slab.
o Analyze what happens to the size and shape of an object when it is heated.
o Analyze qualitatively the effects of conduction, radiation and convection in thermal processes.
Students should understand the kinetic theory model of an ideal gas, so they can:
o State the assumptions of the model.
o State the connection between temperature and mean translational kinetic energy, and apply it to
determine the mean speed of gas molecules as a function of their mass and the temperature of
the gas.
o State the relationship among Avogadro’s number, Boltzmann’s constant, and the gas constant R,
and express the energy of a mole of a monatomic ideal gas as a function of its temperature.
o Explain qualitatively how the model explains the pressure of a gas in terms of collisions with the
container walls, and explain how the model predicts that, for fixed volume, pressure must be
proportional to temperature.
Students should know how to apply the ideal gas law and thermodynamic principles, so they can:
o Relate the pressure and volume of a gas during an isothermal expansion or compression.
o Relate the pressure and temperature of a gas during constant-volume heating or cooling, or the
volume and temperature during constant-pressure heating or cooling.
o Calculate the work performed on or by a gas during an expansion or compression at constant
pressure.
o Understand the process of adiabatic expansion or compression of a gas.
o Identify or sketch on a PV diagram the curves that represent each of the above processes.
Students should know how to apply the first law of thermodynamics, so they can:
o Relate the heat absorbed by a gas, the work performed by the gas and the internal energy change
of the gas for any of the processes above.
o Relate the work performed by a gas in a cyclic process to the area enclosed by a curve on a PV
diagram.
Students should understand the second law of thermodynamics, the concept of entropy, and heat engines
and the Carnot cycle, so they can:
o Determine whether entropy will increase, decrease or remain the same during a particular
situation.
o Compute the maximum possible efficiency of a heat engine operating between two given
temperatures.
o Compute the actual efficiency of a heat engine.
o Relate the heats exchanged at each thermal reservoir in a Carnot cycle to the temperatures of the
reservoirs.
13-1: Atomic Theory of Matter
Atomic and molecular masses are measured in unified atomic mass units (u). This unit is defined so that
the carbon-12 atom has a mass of exactly 12.0000 u. Expressed in kilograms: ________________________
________________________________ describes the continuous random motion of the
atoms in all matter due to a series of collisions.
On a microscopic scale, the arrangements of molecules in ____________ (a),
______________ (b), and _________ (c) are quite different.

13-2: Temperature and Thermometers
________________________ is a measure of how hot or cold something is.
Most materials ____________ when ______________.
Scales for measuring temperature include Celsius (centigrade), Fahrenheit, and Kelvin. The
standard conversion from Fahrenheit to Celsius is
; this can be
rearranged to convert from Celsius to Fahrenheit as
Example 13-2: Taking your temperature
Normal body temperature is 98.6°F. What is this on the Celsius scale?
Exercise A
Determine the temperature at which both sides agree (T C = T F )
13-3: Thermal Equilibrium and the Zeroth Law of Thermodynamics
Two objects placed in thermal contact will eventually come to the same temperature. When they do, we
say they are in ____________________________________.
The _____________________ of thermodynamics says that if two objects are each in equilibrium with a
third object, they are also in thermal equilibrium with each other.
13-4: Thermal Expansion
__________________ changes can yield changes in the ____________ and ______________ of an object.
The change in length is a function of the change in temperature;
o represents the ______________________________________________________ for a material.
o is in ______
o Additionally, the new length of the object can be represented by the equation
Volume expansion is similar, except that it is relevant for liquids and gases as well as solids.
The change in volume is a function of the change in temperature;
o represents the ______________________________________________________ for a material.
o is in ______
o Additionally, the new volume of the object can be represented by the equation

Example 13-3: Bridge expansion
The steel bed of a suspension bridge is 200 m long at 20°C. If the extremes of temperature to which it might be
exposed to are -30°C to +40°C, how much will it contract and expand?
Conceptual Example 13-4: Do holes expand or contract?
If you heat a thin circular ring in the oven, does the ring’s hole get larger or smaller?
Example 13-5: Ring on a rod
An iron ring is to fit snugly on a cylindrical iron rod. At 20°C, the diameter of the rod is 6.445 cm and the inside
diameter of the ring is 6.420 cm. To slip over the rod, the ring must be slightly larger than the rod diameter by
about 0.008 cm. To what temperature must the ring be brought if its hole is to be large enough so it will slip
over the rod?
Conceptual Example 13-6: Opening a tight jar lid
When the lid of a glass jar is tight, holding the lid under hot water for a short time will often make it easier to
open. Why?
Example 13-7: Gas tank in the sun
The 70-L steel gas tank of a car is filled to the top with gasoline at 20°C. The car sits in the sun and the tank
reaches a temperature of 40°C (104°F). How much gasoline do you expect to overflow from the tank?
13-6: The Gas Laws and Absolute Temperature
_________________, _______________, and ________________________ are interrelated for gases.
_______________: At a constant temperature, volume is inversely proportional to pressure.
_______________: At a constant pressure, volume is directly proportional to absolute temperature.
____________________: At a constant volume, pressure is directly proportional to absolute temperature.
13-6: The Gas Laws and Absolute Temperature
Extrapolating, the volume becomes zero at −273.15°C; this temperature is called ____________________.
The concept of absolute zero allows us to define a third temperature scale – the absolute, or Kelvin, scale.
This scale starts with 0 K at absolute zero, but otherwise is the same as the Celsius scale.
The following equation can be used to convert from Celsius to Kelvin____________________________
Conceptual Example 13-9: Don’t throw a closed glass jar into a campfire
What can happen if you did throw an empty glass jar, with lid on tight, into a fire, and why?
13-7: The Ideal Gas Law
The three gas laws are combined in the ideal gas law, , where is the number of
moles of a substance and is the universal gas constant = __________ J/(mol·K) or R = ____________
(L·atm)/(mol·K)

A mole (mol) is defined as the number of grams of a substance that is numerically equal to the molecular
mass of the substance:
o 1 mol H2 has a mass of 2 g
o 1 mol Ne has a mass of 20 g
o 1 mol CO2 has a mass of 44 g
The number of moles in a certain mass of material:
13-8: Problem Solving with the Ideal Gas Law
Standard temperature and pressure (______)
o T = 273 K
o P = 1.00 atm = 1.013 x 10 5 N/m 2
Always measure T in __________
P must be the __________________________________
Example 13-10: Volume of one mol at STP
Determine the volume of 1.00 mol of any gas assuming it behaves like an ideal gas, at STP.
Exercise B
What is the volume of 1.00 mol of ideal gas at 20°C?
Example 13-11: Helium balloon
A helium party balloon, assumed to be a perfect sphere, has a radius of 18.0 cm. At room temperature (20°C),
its internal pressure is 1.05 atm. Find the number of moles of helium in the balloon and the mass of helium
needed to inflate the balloon to these values.
Example 13-12: Estimate mass of air in a room
Estimate the mass of air in a room whose dimensions are 5 m x 3 m x 2.5 m high, at STP.
Exercise C
At 20 °C, would there be more or less air mass in a room than at 0°C?
Example 13-13: Check tires cold
An automobile tire is filled to a gauge pressure of 200 kPa at 10°C. After a drive of 100 km, the temperature
within the tire rises to 40°C. What is the pressure within the tire now?

13-9: Ideal Gas Law in Terms of Molecules: Avogadro’s Number
Since the gas constant is universal, the number of molecules in one mole is the same for all gases. That
number is called Avogadro’s number:
The number of molecules in a gas is the number of moles times Avogadro’s number:
This allows for a restatement of the ideal gas law with Avogadro’s number as _____________, where k is
referred to as Boltzmann’s constant.
Example 13-14: Hydrogen atom mass
Use Avogadro’s number to determine the mass of a hydrogen atom.
Example 13-15: Estimate how many molecules are in one breath
Estimate how many molecules you breathe in with a 1.0-L breath of air.
13-10: Kinetic Theory and the Molecular Interpretation of Temperature
Assumptions of ____________________:
o Large number of molecules, moving in random directions with a ___________________________
o Molecules are far apart, on average
o Molecules obey laws of classical mechanics and interact only when colliding
o Collisions are perfectly _____________
Calculating average force using the average momentum of molecules in a gas, we can apply the ideal gas
law to determine the average kinetic energy.
The root-mean-square velocity can be found from
Example 13-6: Molecular kinetic energy
What is the average translational kinetic energy of molecules in an ideal gas at 37°C?
Example 13-17: Speeds of air molecules
What is the rms speed of air molecules (O 2 and N 2 ) at room temperature (20°C)?
Exercise D
What speed would a 1-gram paper clip have if it had the same KE as a molecule of Example 13-17?