Thermal Physics Flashcards
Thermal expansion coefficient
B = 1/V*dV/dT = d(lnV)/dT
Fourier’s heat conduction law
Rate of heat flow = q(dot) = -kA*dt/dx
k is thermal conductivity.
Virial Equations of State
PV = nRT(1+B/(V/n) + C/(V/n)^2)
Approximation of e^-x for small x
e^-x = 1-x for small x
Van der Waals equation
P=nRT/(V-nb)-a(n/v)^2
Equipartition theorem
At temperature T, the average energy of any quadratic degree of freedom is kT/2.
Total thermal energy
U = NfkT/2
First law
deltaU = q+w
Adiabatic process
No heat transfer between system and surroundings. q=0.
Isothermal
deltaU = 0
Max work
Available when change takes place reversibly
Isothermal + reversible
deltaU = 0, q = -w = nRT*ln(Vf/Vi)
heat capacities
c(v) = q(v)/deltaT = deltaU/deltaT, c(p)=q(p)/deltaT
Work in terms of heat capacity
w=nc(v)deltaT
work + means work done on the gas, compression, T of gas increases
work - means work done by the gas, expansion, T of gas decreases
Latent Heat
q = mL
Enthalpy
H = U+PV
Virial Theorem
In any system where particles are held together by mutual gravitational attraction: U(potential) = -2U(kinetic)
Adiabatic expansion/compression of ideal gas
PV^gamma = constant gamma = (f+2)/f = c(p)/c(v) c(p) = c(v)+R
Mechanical equilibrium
Net force = 0
Temperature
A measure of how easily the multiplicity of the system changes with energy
Stirling’s approximation
ln(N!) = NlnN - N
Approximation of ln(1+x) for small x
ln(1+x) = x for small x
Second law
Any large system in equilibrium will be found in the macrostate with greatest entropy
Boltzmann’s equation
S = kln(multiplicity) in J/K
Spontaneous
deltaS > 0
High temp, large N, entropy estimate
S = Nk(ln(q/N)+1)
In Einstein solid or ideal gas, entropy estimate
S = Nk
Sackur-Tetrode equation
S = Nk(ln(V/N((4pimU)/(3Nh^2))^(3/2))+5/2)
Entropy of mixing
deltaS(A) = N(A)kln(((V(A)+V(B))/V(A)) deltaS(B) = N(B)kln(((V(A)+V(B))/V(B)) deltaS(mix) = deltaS(A)+deltaS(B) = 2Nkln2
Isentropic
deltaS = 0 Isentropic = adiabatic + mechanically reversible
Thermodynamic identity
dU = TdS-PdV+(mu)dN
Thermal interaction
1/T = PartialS/PartialU at constant V,N
Mechanical interaction
P/T = PartialS/PartialV at constant U,N
Diffusive interaction
(mu)/T = - PartialS/PartialN at constant U,V
Third law
Systems cannot absorb energy at T=0. Systems cannot exceed their temperature at maximum entropy. Occurs in systems with finite numbers of energy levels, or a maximum energy U.
Curie’s Law
M = (mu)(N(up)-N(down)) M = N(mu)tanh((mu*B)/kT) M = -U/B tanh(x) = (e^x-e^(-x))/(e^x+e^(-x))
Change in entropy of surroundings
deltaS(surroundings) = -q/T(surroundings) q = U/hfN ? hf is energy difference between ground and excited state
