Work
Thermodynamics
Professor Lee Carkner
Lecture 7
PAL # 6 Equations of State CO2 flow through a pipe
From Table A-1: R = 0.1889 kPa m3 / kg K Tcr = 304.2 K, Pcr = 7.39 MPa
V’1 = (2)(0.1889)(500) / 3000 = 0.06297 m3/s
V’2 = (2)(0.1889)(450) / 3000 = 0.05667 m3/s
1 = m’/V’ = 2/0.6297 =
2 = 2/0.05667 =
PAL # 6 Equations of State Use PR and TR to find Z from chart A-15
PR = P/Pcr = 3/7.39 =0.407 TR1 =500/304.2 = TR2 = 450/304.2 =
V’1 = (0.9791)(0.06297) = 0.06165
2.1% error 1 =32.44, error =2.1 % V’2 =(0.9656)(0.05667) = 0.05472
3.6% error 2 = 36.55, error =3.6 %
Exam #1
Friday, March 24th
Covers: Lectures 1-8 Chapters 1-4
Format: About 10 multiple choice (~25% weight) About 4 problems (~75%weight)
Equations provided Bring just pencil and calculator
Worth 15% of final grade
Work
No displacement, No work
We consider now external work Involves interaction with another system or its
surroundings (external to the system)
Work is a form of energy
Work and Hydrostatic Systems Work is not a property of the system
We need to be able to specify the properties of the system at each point in the process
Called a quasi-equilibrium or quasi-static process
Derivation of Work
Work, Pressure and Volume
W = F ds
W = P dV
If dV is positive (increase in V) then W is positive (work by the system)
Total Work
W = P dV Need to know P as a function of V
Often need to limit or parameterize T
W depends on both the change of volume and how the volume changed
PV Diagram
The process by which the volume changes is a line or curve connecting the two points
For different processes, different curves,
different amounts of work
Path Dependence of Work
Path Dependence What are the paths?
follow isotherm
horizontal
vertical
Closed Cycle
If the system moves from 1 to 2 and then back to 1, it is a cycle
if two different paths are traveled W is the area between the curves
Repeat the same process over and over,
extract work each cycle
Cycle Work
Polytropic Process
Often for compression and expansion of a gas, pressure and volume are related by:
Where C and n are constants
Called a polytropic process Can integrate between points 1 and 2:
For an ideal gas, can replace PV with mRT
Polytrope
Isothermal Process
W = C(1/V) dV = PV ln (V2/V1)
For an ideal gas PV = mRT so PV is constant
Piston of Air
Energy Balance
Qnet,in – Wnet,out =Esystem
Q – W = E First Law of Thermodynamics
We make a distinction between Q and W for eventual use with the second law
Specific Heat
The temperature change due to the energy change can be found with two specific quantities: Specific heat at constant volume
Specific heat at constant pressure
Units of kJ/kg K
cv and cP
Specific Energy
As energy is added to a system the rate of temperature change changes
c tells you the energy needed to effect a change
Temperature Dependence of c
Next Time
Read: 4.4-4.5 Homework: Ch 4, P: 36, 56, 74 Test 1 Friday