Thermodynamics
The Ideal Gas Law Assumptions
• The particles of a gas (atoms or molecules) obey Newton’s laws.
• Particles in the gas move with a range of speeds
• The volume of the individual gas particles is negligible compared to
the volume of the gas.
• The collisions between the particles and the walls of the container
and between the particles themselves are elastic (no kinetic energy
lost)
• There are no forces between the particles (except when colliding).
This means that the particles only have kinetic energy (no potential)
• The duration of a collision is small compared to the time between
collisions.
• The temperature is directly proportional to the average kinetic
energy of the gas particles.
• One mole of an ideal gas contains 6.02x1023 particles and occupies
22.4dm3(L) at Standard Temperature Pressure. (STP T=0ºC and
P=1.01x105Pa.)
Pressure – A reminder
Pressure is defined as the normal
(perpendiculr) force per unit area
P = F/A
It is measured in Pascals, Pa (N.m-2)
Ideal Gas Law Equation
PV  nRT
P = Pressure (N/m2 = Pa)
V = Volume
n = # of moles
R = Universal Gas Constant (8.31Jmol-1K-1)
T = Temperature (K)
simulation
Graphical relationships between
pressure, volume and temperature.
Constant
Constant
Constant
Temperature
Volume
Pressure
P
P
V
V
T
T
Combined Gas Law
PV  nRT
PV
 nR  constant
T
P1V1 P2V2

T1
T2
Example 1:
The internal volume of a gas cylinder is 3.0x10-2 m3.
An ideal gas is pumped into the cylinder until the
pressure is 15MPa at a temperature of 25ºC.
a) Determine the number of moles of the gas in the
cylinder
b) Determine the number of gas atoms in the cylinder?
c) Determine the average volume occupied by one atom
of the gas.
d) Estimate the average separation of the gas atoms.
Example 2:
A sample of gas is contained in a vessel at 20ºC at a
pressure P. What temperature does the gas need to
be heated to in order for the pressure of the gas to be
doubled if the volume remains constant?
Work done on a gas(system) by
a piston.
Gas
Gas
V2
V1
A
Force
F
P
A
F  P(A)
Δx
W  Fx
 P( A) x   P( V )
The First Law of Thermodynamics
• The study of processes in which thermal
energy is transferred as heat and work.
• Applies to engines that convert thermal
energy to mechanical energy.
• Macroscopic view of pressure, volume,
temperature and internal energy in
determining the state of a system.
ΔU ↑
System
System
Q=Thermal
Energy (Heat)
Engine
Engine
WORK
(piston)
(piston)
Q W
U  Q  W
ΔU = The change in internal Energy, which is an
increase in temperature of the System.
First Law of Thermodynamics
U  Q  W
U  Q  PV
All quantities are
measured in joules.
Statement of
conservation of ENERGY
Q = Heat added to system/gas (+) or removed from
system/gas (-)
W = Work done on system/gas (+) or Work done by
system/gas (-). Work is done when there is a change in
volume.
ΔU = increase in internal energy (+) or decrease in internal
energy (-). ΔU represents a temperature change.
Specific Processes and their
corresponding PV graphs
• Isobaric Process – Pressure remains constant
and work is done on the system (-ΔV) or by the
system (+ΔV).
• Isochoric (isovolumetric) Process - Volume
remains constant. No work is done, so there
must be a change in internal energy.
• Isothermal Process – Temperature is constant
and the pressure and volume vary inversely.
• Adiabatic Process – No thermal energy is added
or removed from the system. (Q=0)
Process
Definition
isobaric
constant pressure
PV diagram
P
W
W=PΔV
V
isochoric
constant volume
P
W=0
V
isothermal
constant temperature
P
W=?
V
no heat added or taken
away (ΔU = W)
P
adiabatic
V
Heat Engine
P
C
D
DA
B
CB
A
V
simulation
Heat Engine
• Net work is done by
the gas
• Cycle is clockwise
Heat Pump or
Refrigerator
• Net work is done on
the gas
• Cycle is counterclockwise.
Efficiency
W
Qh  Qc
e

Qh
Qh
Qh = Input Heat (Joules)
Qc = Exhaust Heat (Joules)
W = Work (J)
Maximum Efficiency – Carnot Cycle
Th  Tc
ec 
Th
Th = Maximum temperature in Kelvin
Tc = Minimum temperature in Kelvin
Example:
(a) For part A→B of the cycle, explain whether
(i) Work is done by the gas or work is done on the gas.
(ii) Thermal energy (heat is absorbed by the gas or is ejected from the
gas to the surroundings.
(b) Calculate the work done during the change A→B.
(c) Use the graph to estimate the total work done during one cycle.
(d) The total thermal energy supplied to the gas during one cycle is 120kJ.
Estimate the efficiency of this heat engine.