Download Thermodynamics

Thermodynamics
Intensive and extensive properties
• Intensive properties:
– System properties whose magnitudes are
independent of the total amount, instead, they
are dependent on the concentration of substances
• Extensive properties
– Properties whose value depends on the amount of
substance present
State and Nonstate Functions
• Euler’s Criterion
• State functions
– Pressure
– Internal energy
• Nonstate functions
– Work
– Heat
Energy
• Capacity to do work
• Internal energy is the sum of the total various
kinetic and potential energy distributions in a
system.
Heat
• The energy transferred between one object
and another due to a difference in
temperature.
• In a molecular viewpoint, heating is:
– The transfer of energy that makes use of
disorderly molecular motion
• Thermal motion
– The disorderly motion of molecules
Exothermic and endothermic
• Exothermic process
– A process that releases heat into its surroundings
• Endothermic process
– A process wherein energy is acquired from its
surroundings as heat.
Work
• Motion against an opposing force.
• The product of an intensity factor (pressure,
force, etc) and a capacity factor (distance,
electrical charge, etc)
• In a molecular viewpoint, work is:
– The transfer of energy that makes use of
organized motion
Free
expansion
Isothermal
ΔU
0
q
nRT ln 𝑉𝑓
Isochoric
Isobaric
q+w
𝑉
𝑖
wrev
wirrev
0
𝑉
-nRT ln 𝑉𝑓
0
𝑖
-pextΔV
-pextΔV
Adiabatic
Adiabatic Changes
• q=0!
• Therefore ΔU = w
• In adiabatic changes,
we can expect the
temperature to
change.
• Adiabatic changes can
be expressed in terms
of two steps: the
change in volume at
constant temperature,
followed by a change in
temperature at
constant volume.
Adiabatic changes
• The overall change in internal energy of the
gas only depends on the second step since
internal energy is dependent on the
temperature.
• ΔUad = wad = nCvΔT for irreversible conditions
Adiabatic changes
• How to relate P, V, and T? during adiabatic
changes? Use the following equations!
• ViTic = VfTfc
– Where c = Cv/R
• PiViγ = PfVfγ
– Where γ = Cp/Cv
Adiabatic changes
• What about for reversible work?
• Wad,rev =
𝑛𝑅∆𝑇
1−γ
Free
Isothermal
expansion
ΔU
0
q
nRT ln 𝑓
𝑉𝑖
or -wirrev
Isochoric
Isobaric
Adiabatic
nCvΔT
q+w
w
nCvΔT
nCpΔT or
–wirrev
0
𝑉
wrev
0
wirrev
0
-nRT ln
𝑉𝑓
𝑉𝑖
-pextΔV
0
0
-nRT ln
𝑉𝑓
𝑉𝑖
-pextΔV
−𝑛𝑅∆𝑇
1−γ
=-nCvΔT
=-pextΔV
Exercise
1.
2.
10 g of N2 is obtained at 17°C under 2 atm. Calculate ΔU, q, and w
for the following processes of this gas, assuming it behaves
ideally: (5 pts each)
a) Reversible expansion to 10 L under 2 atm
b) Adiabatic free expansion
c) Isothermal, reversible, compression to 2 L
d) Isobaric, isothermal, irreversible expansion to 0.015 m3 under
2 atm
e) Isothermal free expansion
(Homework) 2 moles of a certain ideal gas is allowed to expand
adiabatically and reversibly to 5 atm pressure from an initial state
of 20°C and 15 atm. What will be the final temperature and
volume of the gas? What is the change in internal energy during
this process? Assume a Cp of 8.58 cal/mole K (10 pts)
1 cal = 4.184 J
Enthalpy
• As can be seen in the previous derivation, at
constant pressure:
• ΔH = nCpΔT
Relating ΔH and ΔU in a reaction that
produces or consumes gas
• ΔH = ΔU + pΔV,
• When a reaction produces or consumes
gas, the change in volume is essentially the
volume of gas produced or consumed.
• pΔV = ΔngRT, assuming constant
temperature during the reaction
• Therefore:
› ΔH = ΔU + ΔngRT
Dependence of Enthalpy on
Temperature
• The variation of the enthalpy of a substance
with temperature can sometimes be ignored
under certain conditions or assumptions, such
as when the temperature difference is small.
• However, most substances in real life have
enthalpies that change with the temperature.
• When it is necessary to account for this
variation, an approximate empirical
expression can be utilized
Dependence of Enthalpy on
Temperature
𝑑𝐻 = 𝐶𝑝𝑑𝑡
𝐻 (𝑇𝑓)
𝑇𝑓
𝑑𝐻 =
𝐻 (𝑇𝑖)
• Where the empirical
parameters a, b, and
c are independent of
temperature and are
specific for each
substance
𝑇𝑖
𝐶𝑝 𝑑𝑡
• Integrate
resulting
equation for Cp
appropriately in
order to get ΔH
Free
expansion
Isothermal
Isochoric
Isobaric
Adiabatic
ΔU
0
nCvΔT
q+w
w
q
nRT ln 𝑓
𝑉𝑖
or -wirrev
nCvΔT
nCpΔT or –
wirrev
0
𝑉
wrev
0
wirrev
0
ΔH
-nRT ln
𝑉𝑓
𝑉𝑖
0
-nRT ln
𝑉𝑓
𝑉𝑖
−𝑛𝑅∆𝑇
1−γ
-pextΔV
0
-pextΔV
=-nCvΔT
=-pextΔV
0 (for ideal
gas)
ΔU
=ΔU + pΔV
=nCpΔT
Adiabatic
Problem
• Calculate the change in molar enthalpy of N2
when it is heated from 25°C to 100°C.
N2(g) Cp,m (J/mol K) a =28.58; b = 3.77x10-3 K;
c = -0.50 x105 K2
Problem
• Water is heated to boiling under a pressure of
1.0 atm. When an electric current of 0.50 A
from a 12V supply is passed for 300 s through
a resistance in thermal contact with it, it is
found that 0.798 g of water is vaporized.
Calculate the molar internal energy and
enthalpy changes at the boiling point.
*1AVs=1J
Thermochemistry
• The study of energy transfer as heat during
chemical reactions.
• This is where endothermic and exothermic
reactions come in.
• Standard enthalpy changes of various kinds of
reactions have already been determined and
tabulated.
Standard Enthalpy Changes
• ΔHƟ
• Defined as the change in enthalpy for a
process wherein the initial and final
substances are in their standard states
– The standard state of a substance at a specified
temperature is its pure form at 1 bar
• Standard enthalpy changes are taken to be
isothermal changes, except in some cases to
be discussed later.
Enthalpies of Physical Change
• The standard enthalpy change that
accompanies a change of physical state is
called the standard enthalpy of transition
• Examples: standard enthalpy of vaporization
(ΔvapHƟ) and the standard enthalpy of fusion
(ΔfusHƟ)
Enthalpies of chemical change
• These are enthalpy changes that accompany
chemical reactions.
• We utilize a thermochemical equation for such
enthalpies, a combination of a chemical equation
and the corresponding change in standard
enthalpy.
• Where ΔHƟ is the change in enthalpy when the
reactants in their standard states change to the
products in their standard states.
Hess’s Law
• Standard enthalpies of individual reactions
can be combined to acquire the enthalpy of
another reaction. This is an application of the
First Law named the Hess’s Law
• “The standard enthalpy of an overall reaction
is the sum of the standard enthalpies of the
individual reactions into which a reaction may
be divided.”
Hess’s Law: Example
Standard Enthalpies of Formation
• The standard enthalpy of formation, denoted as
ΔfHƟ, is the standard reaction enthalpy for the
formation of 1 mole of the compound from its
elements in their reference states.
• The reference state of an element is its most stable
state at the specified temperature and 1 bar.
• Example: Benzene formation
6 C (s, graphite) + 3 H2(g)  C6H6 (l)
ΔfHƟ = 49 kJ/mol
The temperature dependence of
reaction enthalpies
• dH = CpdT
• From this equation, when a substance is
heated from T1 to T2, its enthalpy changes
from the enthalpy at T1 to the enthalpy at T2.
Kirchhoff’s Law
• It is normally a good approximation to assume
that ΔrCpƟ is independent of temperature over
a limited temperature range, but when the
temperature dependence of heat capacities
must be taken into account, we can utilize
another equation
Dependence of Enthalpy on
Temperature
𝑑𝐻 = 𝐶𝑝𝑑𝑡
𝐻 (𝑇𝑓)
𝑇𝑓
𝑑𝐻 =
𝐻 (𝑇𝑖)
• Where the empirical
parameters a, b, and
c are independent of
temperature and are
specific for each
substance
𝑇𝑖
𝐶𝑝 𝑑𝑡
• Integrate
resulting
equation for Cp
appropriately in
order to get ΔH
Kirchhoff’s Law: Example
Exercise