Physics 131 Spring 2006 -- Equations you should know for the final exam
Chapters 14, 15, 17, 18, 19, and 20
Wave velocity v – string tension is F
Wave length λ, wave-vector k
Frequency f, angular frequency ω,period T
Standing wave – separate factors for x and t
Traveling wave – sign determines direction
Normal modes – string fixed at both ends (0,L)
Fluids – buoyant force – density ρ
Pressure = F/A; p vs depth – if y increases
Bernouilli equation – fluid in laminar flow
Work W = ∫ pdV
Heat, work ,energy W = work done by system
Specific heat capacity Q = mcΔT
Molar heat capacity Q = nCΔT
Heat at constant p = heat at constant V + W
Ideal gas law pV = nRT = NkBT
N/n = NA (Avogadro’s number = # molecules
Water: ρ = 103 kg/m3 Tfreeze = 0oC=273.15K
heat flow H = dQ/dt = kAΔT/L k = thermal
Rate of radiative heat transfer (medium 1 to 2)
Thermal expansion ΔL = αL0ΔT
ΔV=βV0ΔT
3
Molecular model of gas KE trans = Nk B T
2
3
Molar specific heat CV = 2 Nk B = 32 nR
(monatomic as in He, Ne) γ = Cp/Cv = 5/3
Adiabatic process means no heat.
Ideal gas
Second ideal gas law: ΔU = nCVΔT
Cyclic process W = area in p-V plane = Qin-Qout
Carnot cycle – heat in at Th, heat out at Tc
2nd Law all heat engines reject heat Qc
Or no heat engine is more efficient than Carnot
Or entropy S depends on state, not path
v = F / μ (μ is mass/length)
k =2π/λ
ω = 2πf = 2π / T and v = λf
y(x,t) = A sin(kx)sin(ωt)
y ( x, t ) = A sin(kx ± ωt ) - for left, + for right
λn = 2L/n nth harmonic has n-1 nodes
FB = W (weight of displaced fluid)=ρV
Upward, then p=p0-ρgy
Av = constant; p + ρgy +½ρv2 = constant
ΔU =Q – W 1st Law Q = heat added to system
c in joules/kg degree K or C
C in Joules/mole degree K or C
Cp = CV + R (ideal gases)
T in Kelvin = T in Celsius + 273.15
per mole) n = m (in g)/M (in amu) = # moles
in a sample of mass m; M is “atomic” mass
Tboil = 100oC = 373.15K
conductivity (W/mK) (A,L) = (area,thickness)
H = dQ/dt = eσA(T14-T24) ( σ in W/m2K4)
Heat of fusion, vaporization: Q = mL
Diatomic molecules also have rotational KE
KE trans + KE rot = 52 Nk B T (neglect vibrational)
CV = 52 Nk B = 52 nR (diatomic as in O2, N2)
γ = Cp/Cv = 7/5
pVγ = constant
U=U(T only)
Efficiency of heat engine e = W/Qin=1-Qin/Qout
No heat (adiabats) in between
Or heat never flows from Tc to Th
Carnot efficiency = 1 - Qc/Qh = 1 – Tc/Th
dS = dQ/T S = ∫ dQ / T (reversible process)