Chapter 2.
The First Law
2011 Fall Semester
Physical Chemistry 1
(CHM2201)
Contents
The Basic Concepts
2.1 Work, heat, and energy
2.2 The internal energy
2.3 Expansion Work
2.4 Heat Transactions
2.5 Enthalpy
2.6 Adiabatic changes
Thermochemistry
2.7 Standard Enthalpy changes
2.8 Standard Enthalpies of formation
2.9 The temperature dependence of reaction enthalpies
State functions and exact differentials
2.10 Exact and inexact differentials
2.11 Changes in internal energy
2.12 The Joule-Thompson effect
System
Surroundings
Universe
Surroundings
The basic concepts
Surroundings
• System : the part of the universe that we are studying
• Surroundings : the rest of universe
The basic concepts
Open: energy and matter can be
exchanged with the
surroundings
Closed: energy can be exchanged
with the surroundings, matter
cannot
Isolated: neither energy nor
matter can be exchanged with
the surroundings
2.1 Work, heat, and energy
Key points
1. Work is done to achieve motion against an
opposing force
2. Energy is the capacity to work
3. Heating is the transfer of energy that makes use
of disorderly molecular motion
4. Work is the transfer of energy that makes use of
organized motion
2.1 Work, heat, and energy
(a) Operational definitions
1. Work (w) : Work is done to achieve
motion against an opposing force
2. Energy : The capacity of the system to do
work
3. Heat (q) : The quantity of energy
transferred as a result of a temperature
difference
4. Exothermic process : releases energy as
heat into its surrounding
5. Endothermic process : energy is required
Adiabatic
Diathermic
2.1 Work, heat, and energy
(b) Molecular interpretation
1. Heating is the transfer of energy that makes use of disorderly
molecular motion (thermal motion) in the surroundings
2. Work is the transfer of energy that makes use of organized motion
in the surrounding
3. The distinction between work and heat is made in the surroundings
2.2 The internal energy
Key points
1. Internal energy (U) is the total energy of a
system
2. Internal energy is a state function
3. The equipartition theorem can be used to
estimate the internal energy
4. The First law
ΔU = U f −Ui
U is the state function in the sense that its value
depends only on the current state of the system
2.2 The internal energy
(a) Molecular interpretation of internal energy
1. Equipartition theorem : the average
energy of each quadratic contribution to
the energy is kT/2
2. k : Boltzmann constant
3
U m (T ) = U m (0) + RT (monatomic gas; translation only)
2
5
U m (T ) = U m (0) + RT (linear molecule; translation and rotation only)
2
U m (T ) = U m (0) + 3RT (nonlinear molecule; translation and rotation only)
•
•
•
•
•
Um = U/n : molar internal energy
Um(0) : molar internal energy at T
N = nNA and R = NAk
3/2RT = 3.7 kJ/mol at 25°C
U of a perfect gas is independent of V
2.2 The internal energy
(b) The formulation of the First Law
1. The First Law of Thermodynamics : The internal energy of an
isolated system is constant
2. Heat and work are equivalent ways of changing a system’s internal
energy
ΔU = q + w
•
•
The change in internal energy of a closed system is equal to the
energy that passes through its boundary as heat or work
‘acquisitive convention’ : q and w are positive if energy is
transferred to the system as work or heat and negative if
energy is lost from the system
2.3 Expansion Work
Key points
1. Expansion work is proportional to the external
pressure
2. Free expansion does not work
3. To achieve reversible expansion, the external
pressure is matched at every stage
dU = dq + dw
2.3 Expansion Work
(a) The general expression
dw = −Fdz
dw = − pex dV
w=−∫
Vf
Vi
pex dV
massless,
frictionless,
rigid,
perfectly fitting
2.3 Expansion Work
(a) The general expression
2.3 Expansion Work
(b) Free expansion
pex = 0 ⇒ w = 0
(c) Expansion against constant pressure
Vf
w = − pex ∫ dV = − pex (V f −Vi )
Vi
w = − pex ΔV
Indicator Diagram
2.3 Expansion Work
(d) Reversible expansion
1. A reversible change : a change that can be reversed by an
infinitesimal modification of a variable
2. Systems at equilibrium are poised to undergo reversible change
3. pex = p should be set at each stage of the expansion to achieve
reversible expansion
dw = − pex dV = − pdV
w=−∫
Vf
Vi
pdV
Consider a sample of gas in thermal and mechanical equilibrium with the surroundings; i.e.,
with Tgas = Tsurroundings and pgas = pexternal. If the external pressure is decreased infinitesimally at
constant T, the gas will expand infinitesimally; if the external pressure is increased
infinitesimally at constant T, the gas will be compressed by an infinitesimal amount.
Strictly speaking, a reversible process cannot be achieved, since to carry out a finite
transformation in a series of infinitesimal steps would require infinite time. All real processes
are therefore irreversible. A reversible process is an idealization (very useful)
2.3 Expansion Work
(e) Isothermal reversible expansion
1. Isothermal, reversible expansion
2. More work is obtained when the expansion is reversible!!!
3. It is because matching the external pressure to the internal pressure
at each stage of the process ensures that none of the system’s pushing
power is wasted
w=−∫
w = −nRT ∫
Vf
Vi
Vf
Vi
pdV
Vf
dV
= nRT ln
V
Vi
2.4 Heat transactions
Key points
1. The energy transferred as heat at constant
volume is equal to the change in internal energy
of the system
2. The heat capacity at constant volume is the slope
of the internal energy with respect to
temperature
dU = dq + dwexp + dwe
dU = dq at constant volume
ΔU = qV
2.4 Heat transaction
(a) Calorimetry
1. Calorimetry : the study of heat transfer
2. Calorimeter : a device for measuring energy transferred as heat
3. Calorimeter constant may be measured electrically by passing a
current, I, of potential difference Δϕ for time, t.
q = CΔT
calorimeter
constant
q = ItΔφ
I : current
t : time
Δϕ : potential diff.
Bomb Calorimeter
2.4 Heat transaction
(b) Heat Capacity
1. Heat capacity : the slope of the tangent to the curve at any
temperature
2. Heat capacity is extensive properties
3. Molar heat capacity at constant volume is intensive property
4. Specific heat capacity is the heat capacity per unit mass
5. Heat capacities depend on the temperature
6. Over small ranges of T at and above room T, the variation is
quite small
" ∂U %
CV = $
'
# ∂T &V
CV ,m = CV / n
dU = CV dT (at constant volume)
ΔU = CV ΔT (at constant volume)
qV = CV ΔT
2.4 Heat transaction
(b) Heat Capacity
1. Large heat capacity : there will be only a small increase in T for
a given quantity of energy transferred as heat
2. An infinite heat capacity : there will be no increases in T
3. At a phase transition, T does not rise as energy is supplied as
heat
4. At a phase transition, the heat capacity of a sample is infinite
" ∂U %
CV = $
'
# ∂T &V
CV ,m = CV / n
dU = CV dT (at constant volume)
ΔU = CV ΔT (at constant volume)
qV = CV ΔT
2.5 Enthalpy
Key points
1. Energy transferred as heat at constant pressure
is equal to the change in enthalpy of a system
2. The heat capacity at constant p is equal to the
slope of enthalpy with T
2.5 Enthalpy
(a) The definition of enthalpy
1. Enthalpy (H) is defined as H = U + pV
2. H is a state function because U, p, and V
are state functions
3. The change in enthalpy is equal to the
energy supplied as heat at constant p
dH = dq
ΔH = q p
2.5 Enthalpy
(b) The measurement of an enthalpy change
1. Isobaric calorimeter : monitors the
temperature change at constant pressure
2. Adiabatic flame calorimeter
3. When a process involves only solids or
liquids, the values of ΔH and ΔU are
almost identical because pVm is so small.
4. Differential scanning calorimeter (DSC)
5. For a perfect gas:
H = U + pV = U + nRT
ΔH = ΔU + Δng RT
2.5 Enthalpy
(c) The variation of enthalpy with T
1. The heat capacity at constant p, Cp : the
slope of the tangent to the a plot of
enthalpy against T at constant p
2. T rises at constant p less than when
heating occurs at constant V because
systems at constant p do work on the
surroundings
3. Cp is larger than Cv
" ∂H %
Cp = $
'
# ∂T & p
dH = C p dT (at constant pressure)
ΔH = C p ΔT (at constant pressure)
q p = C p ΔT
2.6 Adiabatic changes
Key points
1. For the reversible expansion of a perfect gas, p
and V are related by an expression that depends
on the ratio of heat capacities
2.6 Adiabatic changes
1.
2.
Consider the changes that occur when a
perfect gas expands adiabatically
The overall change in internal energy
arises solely from the second step
ΔU = CV (Tf − Ti ) = CV ΔT
wad = CV ΔT
2.6 Adiabatic changes
1.
The physical reason for the difference
between adiabats and isotherms is that
in an isothermal expansion, energy flows
into the system as heat and maintains T;
as a result, p does not fall as much as in
an adiabatic expansion
!V
Tf = Ti ## i
" Vf
1c
$
&&
%
c = CV ,m R
ViTi c = V f T cf
p f V γf = piViγ
γ = C p,m CV ,m