# Thermo I

```Thermodynamics I
AP PHYSICS
RECAP
Thermal Physics
Equations not on the equation sheet
Q  m cT
c  specific heat, units: J/(kg·K)
Q  mL
L  Latent Heat, units: J/kg
The Mole
Quantity in Physics
mass – quantitative measure of object’s inertia
mole – number of particles
Mole & Mass
Every substance has a unique relationship between its mass and number
of moles
Molar Mass (M)
the ratio of the mass of a substance in grams to the number of moles of
the substance
How do you determine Molar Mass?
the mass of 1 mole of a substance equals the atomic mass of the substance
in units of grams rather than atomic mass units
Ex. What is the molar mass of O2?
Methane
What is the molar mass (M) of CH4?
What number of moles (n) are there in 40 g of methane gas?
How many molecules (N) of CH4 does this include?
What is the mass of 24.08 x 1023 molecules of ethanol (C2H5OH)?
Note: n  number of moles
N  number of particles
Ideal Gases: Volume and Number
The behaviors of ideal gases at low pressures are relatively
easy to describe:
The volume V is proportional to the number of moles n and
thus to the number of molecules (this concept stems from
Ideal Gases: Boyle’s Law
Robert Boyle (1627 – 1691)
 Irish physicist and chemist who employed Robert Hooke as an assistant
(you know the Hooke’s law guy and the “cell” guy)
Boyle’s Law
The volume V varies inversely with the pressure P when
temperature (T) and amount of gas (n) are constant.
Ideal Gases: Charles’ Law
Jacques Charles (1746 – 1823)
 French inventor, physicist and hot air balloonist.
Charles’ Law
The pressure P is directly proportional to the absolute
temperature T (temperature in Kelvin) when volume V and
amount n are constant
Ideal Gas Law
Combining of Boyle’s Law and Charles’ Law
R is the ideal gas constant
or R = 0.08206 L∙atm/(mol∙K)
Gas at STP
The condition called standard temperature and pressure (STP) for a gas is
defined to be a temperature of 0oC and a pressure of 1 atm (1.013 x 105
Pa). If you want to keep 1 mole of an ideal gas in your room at STP,
how big is the Tupperware that you need?
[Answer in units of liters, 1 m3 = 1000 L]
Kinetic Theory of an Ideal Gas
Assumptions of the Kinetic-Molecular Model
1.
2.
3.
4.
A container with volume V contains a very large number N of
identical molecules, each with mass m. The container has perfectly
rigid walls that do not move.
The molecules behave as point particles; their size is small in
comparison to the average distance between particles and to the
dimensions of the container.
The molecules are in constant random motion; they obey Newton’s
laws. Each molecule occasionally makes a perfectly elastic collision
with a wall of the container.
During collisions, the molecules exert forces on the walls of the
container; these forces create the pressure that the gas exerts.
Kinetic Theory of an Ideal Gas
For an ideal gas, the average kinetic energy Kavg per molecule is
proportional to the absolute (Kelvin) temperature T.
The ratio R/No occurs frequently in molecular theory and is known as the
Boltzmann constant kB.
What is the value of the Boltzmann constant including units??
Ludwig Boltzmann (1844 – 1906) was an Austrian physicist famous for his founding
contributions in the fields of statistical mechanics and statistical thermodynamics.
Molecular Speeds in an Ideal Gas
If molecules have an average kinetic energy Kavg given by the equation:
Kavg  32 kBT
then what is their average speed???
Five Molecules
Five ideal-gas molecules chosen at random are found to have speeds of
500, 600, 700, 800, and 900 m/s, respectively. Find the rms speed
for this collection. Is it the same as the average speed of these
molecules?
The Boltzmann Constant Gets Around
Starting with the typical ideal gas law (PV = nRT ) derive an expression
for the gas law that includes both the Boltzmann Constant kB and the
number of molecules of an ideal gas N.
Kinetic Energy of A Molecule
What is the average (translational) kinetic energy of a molecule of
oxygen (O2) at a temperature of 27oC, assuming that oxygen can be
treated as an ideal gas?
b) What is the total (translational) kinetic energy of the molecules in 1
mole of oxygen at this temperature?
c) Compare the root-mean-square speeds of oxygen and nitrogen
molecules at this temperature (assuming that they can be treated as
ideal gases).
[mass of oxygen molecule mO2 = 5.31 x 10-26 kg, mass of nitrogen molecule
mN2 = 4.65 x 10-26 kg]
a)
Internal Energy
DWT
Particles in a system (like an ideal gas) are in motion. Therefore:
1.
the particles have some velocity
2.
the particles have some kinetic energy
3.
the system as a whole has some internal energy as a result of the
individual particles’ kinetic energy
This is true of material in any phase (solid, liguid, gas, plasma).
Internal Energy & Temperature
Kinetic Energy of the individual particles
The system as a whole has some internal energy as a result of the
individual particles’ kinetic energy
Kinetic energy of all the particles
First Law of Thermodynamics
DWT
Thermodynamics is the study of energy relationships that involve heat,
mechanical work, and other aspects of energy and energy transfer.
There are two ways to transfer energy to an object:
1. Heat the object
2. do Work on the object
Both of these energy transfer methods add to the internal energy of the object.
The First Law of Thermodynamics (1LT)
Work Done during Volume Change
Classic Thermodynamic System
Gas in a cylinder confined by a piston.
PV Diagrams
Pressure
Area under the curve is the
work done by the gas.
P
Notice the arrow denoting
direction of the process.
Work
Vo
Vf
Volume
Thermodynamic Processes
Four Processes
1. Isothermal
2. Isobaric
3. Isochoric (Isovolumetric)
Isothermal
Pressure
The curve represents pressure as a
function of volume for an ideal gas at
a single temperature. The curve is
called an isotherm.
Pa
For the curve, PV is constant and is
directly proportional to T (Boyle’s
Law).
Pb
Va
For Ideal Gases:
Vb
Volume
Isobaric
Pressure
The curve is called an isobar.
Ta
The pressure of the system
(system - constant amount of
gas, n) changes as a result of heat
being transferred either into or
out of the system and/or work
done on or by the system.
Tb
P
Work
Va
Vb
Volume
isotherms
Ta > T b
Isochoric (Isometric or Isovolumetric)
Pressure
The curve is called an isochor.
Pb
There is no work done in this
process. All of the energy
the internal energy.
Pa
isotherms
V
Volume
Pressure
The curve is called an adiabat.
No heat is transferred into or out
of the system. (An adiabatic curve
Pb
at any point is always steeper than
the isotherm passing through the
same point.)
Pa
Work
Va
isotherms
Vb
Volume
Isobaric Example
Thermodynamics of Boiling Water
One gram of water (1 cm3) becomes 1671 cm3 of steam when boiled
at a constant pressure of 1 atm (1.013 x 105 Pa). The latent
heat of vaporization at this pressure is Lv = 2.256 x 106 J/kg.
Compute:
a) the work done by the water when it vaporizes.
b) its increase in internal energy.
Isochoric (Isovolumetric) Example
Heating Water
Water with a mass of 2.0 kg is held at constant volume in a
container while 10,000 J of heat is slowly added by a flame. The
container is not well insulated, and as a result 2,000 J of heat
leaks out to the surroundings.
a) What is the increase in internal energy?
b) What is the increase in temperature?
[the specific heat of water is 4186 J/kg∙oC]
Molar Heat Capacities
The amount of heat Q needed for a certain temperature change ΔT is proportional
to the temperature change and to the number of moles n of the substance
being heated;
Q = nCΔT
where C is a quantity, different for different materials, called the molar heat
capacity of the material.


Units of C: J/(mol∙K)
Relation of specific heat (c) to molar heat capacity (C) is the molar mass
C = Mc
Because of 1LT the molar heat capacities are not the same for different
thermodynamic processes…
Molar Heat Capacities & 1LT
The molar heat capacities are different for isochoric (constant volume) and
isobaric (constant pressure) processes.
1LT  ΔU = Q+W  Q = ΔU – W
Isochoric
Isobaric
W = -PΔV = 0
For pressure to remain constant the
volume must change
Q = ΔU – o
W = -PΔV
Q = ΔU
All of the heat gained/lost results directly
in a change in internal energy.
Molar heat for a constant volume, Cv
Q = ΔU + PΔV
Some of the heat gained by the system is
converted into work as the system
expands.
Molar heat for a constant pressure, Cp
Relationship between Cv and Cp:
Cp = Cv + R
R  universal gas constant
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