Thermodynamic Systems Physics 313 Professor Lee Carkner Lecture 5

Exercise #3 Equations of State  Ideal gas pressure:  P = RT/v = (8.31)(150)/(1.1733) = kPa   Beattie-Bridgeman pressure:  P = (RT/v 2 )(1-(c/vT 3 ))(v+B)-(A/v 2 )  P = [(8.31)(150)/(1.1733) 2 ][1- ((4.2X10 4 )/(1.1733)(150) 3 )]( )- ( / ) = kPa   Savings  Design A requires = 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/T C )] 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? 