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Unformatted text preview: Lecture 19 Today in Chemistry 260 x •
•
• Recap of Kinetic model, MaxwellBoltzmann distribution
Thermodynamics
First law of thermodynamics x This Week in Chemistry 260 • Reading: 12.3, 12.4; 12.6 (Oxtoby) • Heat capacities, thermodynamics of gases Chemistry 260
Lecture 19
October 21, 2011 • Thermodynaics studies the system from a macroscopic perspective • ClariHies the concept of chemical equilibria (chapter 14). 1 2 What is Pressure? Recap of Kinetic Model PV=nRT P= Rate of change of momenta
Consider one molecule of mass m, with
velocity vx, moving in one dimension,
in a cube of dimension L
Look at the momentum change per
collision with the wall Connects microscopic properties (speed, # collisions, etc.) to macroscopic properties (volume, pressure, temperature, etc.) Based on ideal gas assumptions: • Molecules very small, don't interact, have random motion, elastic collisions • Pressure related to speed • Temperature related to average kinetic energy force mass × acceleration
=
area
area Pressure and speed of
1
⇒ PV = Nms 2 molecules
related
3 Etrans = 3
k BT
2 Temperature is essentially a measure of the
average kinetic energy of the atoms/
3
molecules in the gas Clarification on Maxwell Distribution of Speeds ⇒ urms = 1
2 To 2 RT
M 8 RT
πM
3RT
M L
L −mv x = 2mv x Δvx = vf ‒ vi
For an elastic collision, vf=vi
Δvx = vx ‒ vx =2vx All particles at vxΔt distance will hit the wall.
This amount to volume of L2 vxΔt
(N number density = N/V)
Only half of the particles move at the right direction ½* N L2 vxΔt
Total momenta change *= (momentum change per collision) m N L2 vx2Δt
Rate of change of the momenta (Divide by Δt): m N L2 vx2
Pressure = Rate of momenta change / Area 3
Etrans = kBT ⇐
2 1
PV = Nms 2 ⇐
3 First P= Nm 2
× vx
L3 4 a warning Definitions and Terminology: 3 ⎛ m ⎞ 2 2 − mu 2 2 kBT
f ( u ) = 4π ⎜
⎟ ue
⎝ 2π k BT ⎠ ⇒u = 1.
2.
3.
4.
5.
6. ) mv x Thermodynamics The Maxwell Distribution of Speeds gives us
information regarding how speed and temperature are related.
Developed specifically for IDEAL GASES
Similar expressions exist for other phases ⇒ ump = ( s = v2 + v2 + v2
x
y
z L velocity = vx System
Surroundings
State
State Function
Intrinsic
Extrinsic
Endothermic
Exothermic
Heat Maximum (peak) average root mean square 5 Work
Adiabatic
Diathermic
Closed System
Open System
Isolated System
Reversible
Irreversible
Kinetic Energy Potential Energy
PV Work
Internal Energy
Enthalpy
Entropy
Heat Capacity
Specific Heat
Free Energy
Spontaneous Negative work is done by the system on the surroundings
Positive work is done by the surroundings on the system 6 1 Lecture 19 Today:
First law of thermodynamics,
energy conservation
Thermal equilibration
Definitions and Terminology:
Work
System
Adiabatic
Surroundings
Diathermic
State
Closed System
State Function
Open System
Intrinsic
Isolated System
Extrinsic
Reversible
Endothermic
Irreversible
Exothermic
Kinetic Energy
Heat Thermodynamics Thermodynamics Consider a system  such as a piston dx
Potential Energy
PV Work
Internal Energy
Enthalpy
Entropy
Heat Capacity
Specific Heat
Free Energy
Spontaneous Negative work is done by the system on the surroundings
Positive work is done by the surroundings on the system Opposing Force system CH 4 + 2O 2 ⎯⎯⎯ CO 2 + 2H 2O
→
The piston does work
causing your car to move.
7 A Thermodynamic State How do we describe such a process? A Thermodynamic State The State of a thermodynamic system is defined by its properties
(Defines the conditions of the MACROSCOPIC system that has EQUILIBRATED)
The ideal gas law is an equation of state. PV = nRT
The van der Waals equation is an equation of state.
(P+an2/V2)(Vnb) = nRT P,V,T P,V,T Systems with the same properties are in
identical thermodynamic states.
Volume,
Temperature,
Pressure, and
quantity (n) are
examples of state
functions. P,V,T State functions are
pathindependent,
independent of the
history of the system. The state is defined by the
properties P,V,n, and T
Constant mass and pressure
9 A State Function 8 10 Like altitude, it doesn t matter how you get up there. The key players in the first law of thermodynamics
(conservation of energy): U=Q+W DU = q + w
• U – internal energy (state)
• Q – heat
• W – work 11 14 2 Lecture 19 Work Work Mechanical work is done when a mass is accelerated. Definition: Work is defined as energy
deposited into the uniform macroscopic
motion of a large number of particles.
NOT a state function ‒ path dependent 1. Mechanical Work:
2. Surface Work:
3. Electrical Work
4. Expansion Work: dw=Fdx
dw=ϒdA
dw= εdQ
dw=PdV F m (Force×distance )
(Surface tension×area)
(electrical potential×charge)
(external pressure×volume) A B
x
dw = Force × Distance
dw = m ax dx Work – energy theorem:
w = ΔKE, change in kinetic energy of the system
15 Work 16 PressureVolume (PV) Work Mechanical work is done when a mass is accelerated. surroundings m
F m m
B A dx y
system x dw = PEX dV Negative work is done by the system on the surroundings
Positive work is done by the surroundings on the system Constant External Pressure: w = PEX ΔV 18 Energy may be exchanged with the surroundings in the form of work Opposing Force Fx
AREA By convention: Work – energy theorem:
w = ΔKE + ΔPE
ΔPE = m g dy
w = change in kinetic energy plus change in
potential energy of the system dx PEX = dw = PEX A dx w = Force × Distance Work dw = Fx dx 19 Heat Definition: Heat is defined as energy
deposited into the microscopic random
motion of the particles.
NOT a state function ‒ path dependent Constant External
Pressure:
w = PEX ΔV A diathermic wall is one that ALLOWS for heat transfer. system An adiabatic wall is one that DOES NOT ALLOW for heat transfer. But system or surroundings often get HOT…
Heat Energy may be exchanged with the surroundings in the form
of heat
T1 T2 Amount of heat exchanged is q
measured in energy units
20 21 3 Lecture 19 Equilibrium Thermodynamics (definitions) • Open System
mass, heat, energy flow freely
• Closed System
heat, energy flow freely System ΔU = q + w • Isolated System
no mass, heat, or energy flow
• U – internal energy (state)
• Q – heat
• W – work System System HEAT HEAT q>0 q<0
Exothermic Endothermic 22 U: ‒ KE of the molecules
‒ PE between molecules
‒ Bond energies Internal Energy 23 First Law of Thermodynamics/ energy conservation ETotal = KE + PE + U U = Sum Total Internal Energy U: ‒ KE of the molecules
 PE between molecules
 Bond energies The sum of all of the kinetic and potential energy contributions to
the energy of all the atoms, ions, molecules, etc. in the system. He gas Methanol Gas ΔU = q + w for a closed system
ΔU = 0 for an isolated system Conservation of Energy
The change in internal energy (ΔU) of a closed system is
equal to the sum of the heat (q) added to it and the work
(w) done upon it.
The internal energy of an isolated system is constant. Translational Energy Rotational Energy Electronic Energy Vibrational Energy Nuclear Energy Bond Energy Internal energy is a state function.
 Quantity is independent of path.
24 25 First Law of Thermodynamics ΔU = q + w Summary of Thermodynamics
closed system
expansion against
external pressure 0 PΔV qv qp ΔU=w+q heat introduced Constant
Pressure q q Constant
Volume w=PΔV closed system
constant volume Process qv Constant
Temperature Adiabatic Constant
Nothing qpPΔV Value T w = PΔV = 0 no work done
U ✓ ΔU = qv ΔU = q + w = q  PexΔV
Heat energy is stored as internal
energy and released as work. 26 27 4 Lecture 19 H =U + PV Enthalpy Enthalpy is a description of the thermodynamic potential of a system.
It is frequently most convenient to
carry out a process at constant
pressure. H ≡ U + PV ΔH = Δ (U + PV )
ΔH = ΔU + Δ( PV )
At constant pressure: ΔH = ΔU + PΔV
ΔH = ΔU + PΔV = qp • synthesizing a compound in lab
• cooking dinner
• drying the laundry ΔU = q + w At constant pressure
if only PV work is done:
General
statement Vf ΔU = q p − P ∫ dV
Vi ΔU = q p − PΔV
q p = ΔU + PΔV At constant pressure assuming only PV work:
Change in Enthalpy is the heat transferred8in
2
the process H= U + PV Enthalpy Enthalpy is a description of the thermodynamic potential of a system. H ! U + PV
U, P and V are all state functions
H is a state function
In general: ΔH = ΔU + Δ( PV ) ΔU, P and V are all state functions
ΔH is a state function
At constant pressure: ΔH = ΔU + PΔV
q p = ΔU − w Amount of thermal
energy being absorbed Change in
internal energy Amount of energy going
29
into expansion work 5 ...
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