Peter Atkins • Julio de Paula
Atkins’ Physical Chemistry
Eighth Edition
Chapter 2
The First Law
Copyright © 2006 by Peter Atkins and Julio de Paula
Homework Set #2
Atkins & de Paula, 8e
Chap 2 Exercises: all part (b) unless noted
2, 3, 4, 7,
8, 12, 13, 15
19, 21, 23, 25
Fig 2.1 Types of Systems
Fig 2.2 Comparison of Adiabatic
and Diathermic Systems for
Exo- and Endothermic Processes
Fig 2.3 Thermal energy from system to surroundings
Fig 2.4 System does work on surroundings
Equivalent Expressions of the First Law:
• Conservation of energy
• In terms of heat and work
• Formal statement
Internal Energy
• Internal energy, U, is the total kinetic and potential
energy of the molecules in the system
• Approximated by the equipartition theorem:
• Each degree of freedom contributes ½ kT to U
• Degrees of freedom are associated with:
• translation, rotation, and vibration
Kinetic Energy of Translational motion:
EK 
2
1
mv
x
2
 21 mv 2y  21 mv 2z
• According to the equipartition theorem, the mean trans
energy for one molecule is 3/2 kT
• EK = 3/2 RT for one mole of molecules
• ∴ Um = Um(0) + 3/2 RT
• where Um(0) ≡ molar internal energy at T = 0
Fig 2.5 Rotational modes of molecules and
corresponding average energies at temperature T
Linear
Um = Um(0) + 5/2 RT
Nonlinear
Um = Um(0) + 3 RT
First Law in terms of conservation of energy:
• The internal energy of an isolated system is constant
• No ‘perpetual motion machine’ can exist
Waterfall
by M.C. Escher
First Law in terms of conservation of energy:
• The internal energy of an isolated system is constant
• No ‘perpetual motion machine’ can exist
First Law in terms of heat and work:
• ΔU = q + w (Internal energy is a state function)
• i.e., heat and work are equivalent ways of changing U
Illustration of change in
internal energy, ΔU,
as a state function.
Formal Statement
of First Law:
The work needed to change an
adiabatic system from one state
to another is the same however
the work is done.
Fig 2.6 General expansion work
• Focus on infinitesimal
changes
• ΔU = q + w becomes
dU = dq + dw
When gas expands:
dw  Pex dV
f

w   Pex dV
i
Irreversible expansion
Fig 2.7 Work done by a gas
when it expands against a
constant external pressure
f

w   Pex dV
i
f

 Pex dV   Pex ( Vf  Vi )
i
w  Pex ΔV
Reversible expansion
Fig 2.8 Work done by a gas
when it expands isothermally
against a non-constant external
pressure.
• Set Pex = P at each step of
expansion
• System always at equilibrium
f

w   Pex dV
i
• Since Pex is not constant, it
can’t be brought out
Isothermal reversible expansion
f

w   Pex dV
i
• Since Pex is not constant, it can’t be brought out
• However, Pex depends on V, so substitute using PV = nRT
f
dV
w  nRT
V

i
Vf
 nRT ln
Vi