Pure Substances Thermodynamics Professor Lee Carkner Lecture 5.
Volume Changes Physics 313 Professor Lee Carkner Lecture 19.
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Transcript of Volume Changes Physics 313 Professor Lee Carkner Lecture 19.
Exercise #18 Steam Tables
Boiling water at low pressure From chart P = 75 kPa, T = 91.78 C and T = 100 kPa,
T = 99.63 C
Cover with heavy lid Plid = F/A = mg/r2 = [(4)(9.8)/()(0.1)2] = 1.25 kPa Now have a factor of 0.384 between table values
http://www.chempute.com/waspwin.htm
Solids
Solids will hold a volume even in conditions of low external pressure
Need to be able to accurately measure small changes to find expansivity and compressibility
Volume Expansivity How does the size of a a solid object change
with temperature? Need to find volume expansivity
For isotropic materials:
where is the linear expansivity:
= (1/L)(dL/dT) Note that some materials are non-isotropic
Optical Interferometer To find and thus need to measure
small change in linear dimension
Separate two semi-transparent plates with a ring of the material in question
Each interference fringe that moves past a reference point indicates ½ wavelength of changed size
Determining
If N fringes pass the field of view, than the change in size (from L0 to L) is:
The relative change is:
(L - L0)/L0 = ½N / L0
Or: = d/dT (½N / L0)
Variation of with T
Rises sharply with T and then
flattens out
Variations are only weakly
dependant on pressure (for solids)
Compressibility
How does volume change with pressure?
= -(1/V)(dV/dP)
Adiabatic compressibility is also isentropic
Determining s
The adiabatic compressibility can be found for a fluid by measuring the speed of sound (pressure) waves
For a crystal solid have to measure both shear and pressure waves
and S
How are and s related? by the heat capacities:
cP –cV = Tv2/
We can combine equations to get:
-S = Tv2/cP
Variations of with T
Unlike approaches a constant at 0 K
Values tend to rise linearly at higher T for solids
Liquids generally have an exponential rise of with T:
Liquids also have a linear increase of
with P
Heat Capacity at Constant Volume
Can find cV with Mayer relation How does cV (molar heat capacity) vary with
temperature?
At the Debye temperature, cV approaches 3R
For all substances, cV versus T curves have a similar shape, but each substance may have different Debye temperatures
Entropy and Heat Capacities
How are the entropy and heat capacities related?
dS = dQ/T
(dQ/dT) = T (dS/dT)
Can calculate entropy change from C:
Where C is CP or CV depending on if the process is isobaric or isochoric