Thermodynamic Systems Physics 313 Professor Lee Carkner Lecture 5.
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Thermodynamic Systems
Physics 313Professor Lee
CarknerLecture 5
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
Temperature Dependence
Can use the equation of state to find dependence
Can use differential theorems to relate
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.)
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
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
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?
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
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•
Oil on Water
A film of oil on water increases the surface tension:
( - w)A = aT
Sort of a 2-D equation of state
Electrochemical Cell
A battery produces emf through chemical reactions
The emf depends on the amount of charge transferred
Batteries can be recharged
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
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
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
The Eagle Nebula - Interstellar Dust
Paramagnetism and Interstellar Dust
Intensive Extensive
Independent of mass
Tension emf Magnetic field
Proportional to mass Length Charge Total magnetization
Concepts
How do system properties vary with temperature?
What are the differential relations?
How can the differential relations be rewritten?
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