ChemE 260 Work and Heat

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ChemE 260 Work and Heat

• Dr. William Baratuci
• Senior Lecturer
• Chemical Engineering Department
• University of Washington
• TCD 4 A BCB 3 1 4, pg 150 - 155

April 11, 2005
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Work

• Definition
• A force acting through a distance
• A restraining force is overcome to move an object
• Boundary Work or PV Work F P A
• Thermodynamic Definition of Work
• Work is done by a system on its surroundings if
  the sole effect of a process on its surroundings
  could have been raising a weight.
• This definition allows for other forms of work,
  such as spring work, electrical work
  gravitational work and acceleration work.

Baratuci ChemE 260 April 11, 2005
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Sign Convention for Work

• increases as T increases, so changes in
  have a natural sign.
• This is not true for work
• A system can do work on the surroundings or the
  surroundings can do work on the system
• We choose which is positive and which is
  negative. We choose a sign convention.
• In this course we choose work done BY the system
  on the surroundings to be positive
• Always include an arrow for work on our sketches
  to indicate thesign convention we are using.

System
WORK
Baratuci ChemE 260 April 11, 2005
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Power Path Variables

• Power the rate at which work is done
• Exact Differentials
• State variables U ? dU
• Changes in state variables, like U, do not depend
  on which process path the system follows between
  2 states
• Inexact Differentials
• Path Variables W ? ?W
• Systems do not have work
• Work is a form of energy that only exists as it
  moves across a system boundary.
• W12 depends on the path the process follows from
  state 1 to state 2.
• Use ? instead of d for inexact differentials of
  path variables

Baratuci ChemE 260 April 11, 2005
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Boundary Work and Process Paths
P2 gt P1 V2 lt V1 T2 gt T1
P2 gt P3 gt P1 V3 V2 T3 T1
Adiabatic Compression Q 0
Isochoric Cooling
P1, V1, T1
Adiabatic Compression Q 0
Isochoric Cooling
P3 gt P1 gt PA V3 lt V1 T3 T1
PA lt P1 VA V1 TA lt T1
P1, V1, T1
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Process Paths on a PV Diagram
2
3
P
1
T2
T1
TA
A
Baratuci ChemE 260 April 11, 2005
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Boundary Work on a PV Diagram
2
3
P
1
T2
T1
TA
A
Baratuci ChemE 260 April 11, 2005
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Boundary Work on a PV Diagram
2
3
P
1
T2
T1
TA
A
Baratuci ChemE 260 April 11, 2005
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Quasi-Equilibrium Processes

• Does it matter how rapidly we compress the gas in
  steps 1-2 and A-3 ? Yes !
• When a gas is rapidly compressed
• The molecules cannot get out of the way of the
  piston rapidly enough
• As a result, the local pressure right in front of
  the piston is greater than the pressure in the
  bulk of the gas.
• Presist gt Pbulk
• As a result, Pfast gt Pslow
• Quasi-Equilibrium Processes
• Infinitely slow
• Always in an equilibrium state, Presist Pbulk

Baratuci ChemE 260 April 11, 2005
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Wb for Special Types of Processes

• Isobaric
• Isothermal IG
• Polytropic
• ? 1 isothermal !
• ? ? 1
• Polytropic IG

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Heat Q

• Another form of energy in transition across a
  system boundary, like work.
• Flows spontaneously from hot to cold
• Heat is the flow of thermal energy while U is the
  amount of thermal energy a system holds.
• Heat is comparable to electrical current while U
  is comparable to electrical potential or voltage.
• Sign Convention
• Heat flow into a system gt 0

Baratuci ChemE 260 April 11, 2005
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Heat A Few Details

• Heat is a path variable and the differential of
  heat is inexact, so we use ?
• In an adiabatic process Q 0
• If the heat transfer rate, , is constant,
  then
• Heat Flux

Baratuci ChemE 260 April 11, 2005
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Conduction

• Fouriers Law
• k thermal conductivity W/m-K
• If k constant
• Magnitude of k
• Metals k ? 100 W/m-K
• Non-metals k ? 1 - 10 W/m-K
• Liquids k ? 0.1 - 10 W/m-K
• Gases k ? 0.01 0.1 W/m-K
• Insulation k ? 0.01 0.1 W/m-K

Baratuci ChemE 260 April 11, 2005
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Convection Heat Transfer

• Convection is the combination of conduction and
  fluid motion
• For the same fluid and conditions Qconv gt Qcond
• Forced Convection
• Fluid motion is driven by an external force, such
  as pressure
• Free or Natural Convection
• Fluid motion is driven by density differences and
  buoyant forces

Baratuci ChemE 260 April 11, 2005
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Newtons Law of Cooling

• Hot surface
• Cold surface
• h convection heat transfer coefficient
  W/m2-K
• Depends on fluid and surface properties
• Depends on the nature of the fluid velocity
  profile
• Magnitude of h
• Free convection, gases h ? 2 - 25 W/m2-K
• Free convection, liquids h ? 50 - 1000 W/m2-K
• Forced convection, gases h ? 25 - 250 W/m2-K
• Forced convection, liquids h ? 50 20,000
  W/m2-K
• Boiling phase change h ? 2500 1x105 W/m2-K

Baratuci ChemE 260 April 11, 2005
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Radiation Heat Transfer

• Atoms emit photons in the infrared part of the
  spectrum. The photons carry thermal energy to
  the surface that absorbs them. ?
  emissivity We usually assume ? 1
• Radiation exchange between a body its
  surroundings If ? 1Boldly assume ? body ?
  surr ?

Baratuci ChemE 260 April 11, 2005
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Example 1

• Air undergoes a three-process cycle. Find the
  net work done for 2 kg of air if the processes
  are
• Process 1-2 constant pressure expansion
• Process 2-3 constant volume cooling
• Process 3-1 constant temperature compression
• Data T1 100oC T2 600oC P1 200 kPa
• Answers W12 287 kJ, W23 0 kJ, W31 -182
  kJ Wcycle 105 kJ

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Next Class

• 1st Law of Thermodynamics
• Energy is neither created nor destroyed
• One of the 2 most important relationships in this
  course
• Problem Solving Proceedure
• A system to help avoid overlooking important
  aspects of a problem
• Saves time on unfamiliar problems

Baratuci ChemE 260 April 11, 2005