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Thermodynamic Systems
Physics 313Professor Lee
CarknerLecture 5
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Exercise #3 Equations of State
Ideal gas pressure: P = RT/v = (8.31)(150)/(1.1733) = 1062.39 kPa
Beattie-Bridgeman pressure: P = (RT/v2)(1-(c/vT3))(v+B)-(A/v2) P = [(8.31)(150)/(1.1733)2][1-((4.2X104)/(1.1733)(150)3)]
(1.1733+0.05076)-(133.193/1.17332) = 999.84 kPa
Savings Design A requires 1062.39-999.84 = 62.55 kPa more
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Temperature Dependence
Can use the equation of state to find dependence
Can use differential theorems to relate
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Generic Relations
Consider a system with interdependent properties x, y and z:
dz = (z/x)y dx + (z/y)x dy
(x/y)z = 1/( y/ x)z
(x/y)z(y/z)x = -(x/z)y
Can use these along with: Tabulated x,y,z dependencies (expansivity, bulk
modulus etc.)
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Stretched Wire A wire under tension is a
thermodynamic system that can be described with three variables:
differential changes can be related by:
dL = (L/T) dT + (L/)T d
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Wire Relations
Linear Expansivity:
= (1/L)(L/T)
Isothermal Young’s Modulus:
Y = (L/A)(/L)T
These are well known for most normal conditions
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Wires and Sound Vibrating strings can produce notes of a
given frequency
Frequency depends on wave speed and wavelength, which are properties of the string:
is usually fixed
based on string (linear density) is usually fixed
How does the tension change?
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Surfaces Surfaces (such as films) act like 2-D wires
The surface tension is a force that pulls in the plane of the surface
Surface tension relations often depend on the type of system
e.g. vapor above liquid, oil film on water
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Boundaries as Surfaces
For surface defined as the boundary between a liquid and its vapor:
= 0[1 - (T/TC)]n
where: •
• n is between 1 and 2
• Higher T means lower tension•
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Oil on Water
A film of oil on water increases the surface tension:
( - w)A = aT
Sort of a 2-D equation of state
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Electrochemical Cell
A battery produces emf through chemical reactions
The emf depends on the amount of charge transferred
Batteries can be recharged
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Equation of State We can relate the emf to 2 other variables
The equation of state is: = 20 + (T-20) + (T-20)2 + (T-20)3
Constants depend on materials and chemicals
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Dielectric Slab Material in an electric field will undergo polarization
(molecules become polar) The total polarization depends on the electric field and
the temperature
Equation of state:P/V = [a + (b/T)]E
Where P/V is the polarization per unit volume
Thermal “forces” compete with electrical
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Paramagnetic Rod Paramagnetic materials develop magnetization in a
magnetic field
Non-magnetic materials become magnetic
Properties:
Equation of state:M = CH/T
M decreases at higher temperature
This assumes a long thin shape
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The Eagle Nebula - Interstellar Dust
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Paramagnetism and Interstellar Dust
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Intensive Extensive
Independent of mass
Tension emf Magnetic field
Proportional to mass Length Charge Total magnetization
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Concepts
How do system properties vary with temperature?
What are the differential relations?
How can the differential relations be rewritten?