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Pure Substances
Physics 313Professor Lee
CarknerLecture 18
Exercise #17 Isenthalpic For the initial state
Pi = 5 MPa, Ti = 115 K Extrapolating we get:
s1 = 4.9945 kJ/ K kg and h1 = 232.3 kJ/kg Isenthalpic process so sf = si
For sf =4.9945 and Pf = 1 MPa, what is hf? s(1 MPa and 110 K) = 4.875, s(1 MPa and 120
K) =
hf = 222.8 P = mh = mh = (118.2)(232.3-222.8) =
Annual energy form turbine = (1123 kW)(8769 hr/year) = 9.84X106 kWh (9.84X106 kWh) ($0.075 per kWh) =
Brian Greene to Speak Next Week
Author and host of “The Elegant Universe”
Expert on String Theory A “theory of everything”
Monday May 3, 7:00pm, Olin Auditorium “Breakthrough: Challenging What We Know”
Tuesday, May 4, 10:30am, 102 Science Informal discussion with students and faculty
Go to one or the other and sign in, get 3 points extra credit on final exam
Substances
A pure substance is either: A homogenous mixture of several elements
PV and PT diagrams produce curves
separating phases PVT diagrams have surfaces as
boundaries
PV Diagram
The phase of a substance depends on its position on the PV diagram
Each point on the PV diagram represents:
Saturation
The substance has to be at the saturation temperature for the pressure (or visa versa) in order to change phase
Critical Point
Where the saturation curves intersect is the critical point
At temperatures higher than this there is no distinction between liquid and gas
Above the critical isotherm, no amount of pressure can condense the vapor to a liquid
Steam Tables PV and PT diagrams contain important
information about substances
We often want specific information, but there may be no equation available and we don’t want to read off a graph
Sometimes called steam tables
Have to extrapolate between values
PT Diagram Three curves can be drawn on the PT diagram
Fusion curve
Vaporization curve
Sublimation curve
The curves bound three distinct regions, one for each phase
Juncture of the three curves is the triple point where all three coexist
Other PT Features
An isobar at standard atmospheric pressure intersects the normal boiling and melting points
The critical point is on the vaporization curve
Gas above critical T is called “gas”, below it is called “vapor”
Triple Points Different solid phases are possible
Called polymorphs
Triple point is a point where any three phases coexist
The triple point is a triple line on a PV diagram
PVT Diagram
Surfaces define volume regions where phases are allowed
Have a series of PT diagrams, one for each volume
Types of PVT Curves
Substance does not change much with volume
Volume increase indicates density decrease
4He has two different liquid phases and
two triple points for a given volume
Equations of State
The ideal gas law holds for low pressures
Finding Critical Point What defines the critical point?
(P/ V) = 0(2P/V2) = 0
These two equations plus the equation of state itself gives you three equation and three unknowns Substitute TC, PC, VC for T, P and V and solve
Molar Heat Capacity Heat capacity at constant pressure
can be found by heating a sample at a uniform rate at constant pressure
Consider molar heat capacity cP is zero at absolute zero and rises
with T
Debye Temperature For 1 mol of a solid a certain number of
atoms will be vibrating in the crystal lattice
Called the Debye temperature cP falls rapidly below Debye temperature