1. ChemE 260 Work and Heat Dr. William Baratuci Senior Lecturer
Chemical Engineering Department
University of Washington
TCD 4: A & B CB 3: 1 – 4, pg
April 11, 2005

2. Work Definition Boundary Work or PV Work: F = P A
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

3. 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 the sign convention we are using.
System
WORK
Baratuci
ChemE 260
April 11, 2005

4. 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

5. Boundary Work and Process Paths1 2 3
P2 > P1
V2 < V1
T2 > T1
Adiabatic
Compression
Q = 0
Isochoric
Cooling
P2 > P3 > P1
V3 = V2
T3 = T1
P1, V1, T1 1 A 3
Isochoric
Cooling
Adiabatic
Compression
Q = 0
P3 > P1 > PA
V3 < V1
T3 = T1
PA < P1
VA = V1
TA < T1
Consider the two processes shown here: and 1-A-3
U, H and V are the same for each of these processes because they begin and end at the same states.
But, is the amount of boundary work the same for both processes ?
The easiest way to tell is to plot the process path on a PV Diagram
Then, make use of the fact that boundary work is the integral of P dV to determine if the boundary work done by the two processes are the same.
P1, V1, T1

6. Process Paths on a PV Diagram2 3 P 1 T2 T1 TA A V ~
Baratuci
ChemE 260
April 11, 2005

7. Boundary Work on a PV Diagram2 3 P 1 T2
The shaded area is the boundary work done during the process
Is this work positive or negative under our sign convention ? T1 TA A V ~
Baratuci
ChemE 260
April 11, 2005

8. Boundary Work on a PV Diagram2 3 P 1 T2
The shaded area is the boundary work done during the process 1-A-3.
Is this work positive or negative under our sign convention ?
The amount of boundary work is NOT equal for the two processes !
This is because work depends on the process path.
Work is a PATH variable, NOT a property or state variable like V, U and H.
What about heat ? Is the heat transfer for the two processes the same ?
Nope. Heat is also a PATH variable. T1 TA A V ~
Baratuci
ChemE 260
April 11, 2005

9. 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 > Pbulk
As a result, Pfast > Pslow
Quasi-Equilibrium Processes
Infinitely slow
Always in an equilibrium state, Presist = Pbulk
Baratuci
ChemE 260
April 11, 2005

10. Wb for Special Types of Processes
Isobaric:
Isothermal & IG:
Polytropic:
 = 1: isothermal !
  1:
Polytropic & IG:
Isobaric is the easiest type of process when it comes to evaluating the boundary work.
Evaluating Wb for an isothermal process isn’t easy unless the fluid in the system is an ideal gas. Then, it isn’t bad at all
Notice that the last equality is true because P1V1 =P2V2 for an IG undergoing a polytropic process.

11. 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 > 0
Baratuci
ChemE 260
April 11, 2005

12. 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

13. Conduction Fourier’s Law: k = thermal conductivity [=] W/m-K
If k = constant:
Magnitude of k:
Metals: k  100 W/m-K
Non-metals: k  W/m-K
Liquids: k  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

14. Convection Heat Transfer
Convection is the combination of conduction and fluid motion
For the same fluid and conditions: Qconv > 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 Tf TS
Velocity
Profile
Temperature
TS > Tf
T = Tf
Baratuci
ChemE 260
April 11, 2005

15. Newton’s 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  W/m2-K
Free convection, liquids: h  W/m2-K
Forced convection, gases: h  W/m2-K
Forced convection, liquids: h  50 – 20,000 W/m2-K
Boiling phase change: h  2500 – 1x105 W/m2-K
Remember that q = heat flux.
Baratuci
ChemE 260
April 11, 2005

16. 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  = 1: Boldly assume  body =  surr =  :
T must be expressed in Kelvins or Rankine (an absolute T-scale.
Emissivity is a measure of the ability of a surface to emit thermal radiation
s = Stefan-Boltzmann Constant = 5.67 x 10-8 W/m2-K4.
Baratuci
ChemE 260
April 11, 2005

17. 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

18. Next Class 1st Law of Thermodynamics Problem Solving Proceedure
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