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?