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