6.1: Atmospheric Pressure
m = weight/6.022*1023
a) p2/p1 = 1/2 because the partial pressure falls to 1/2 at sea level
a) p2/p1 = 1/2 = exp-(mgh/kT)
b) p2/p1 = 1/2 = exp-(mgh/kT)
6.2: Atoms on Surfaces
F = U - TS ... U = -N*Δ ... S = k*ln(Ω) ... ln(Ω) = N(ln(M/N)+1)
a) F = -NΔ1 - T*k*N(ln(M1/N)+1)
b) F = -NΔ2 - T*k*N(ln(M2/N)+1)
c) kT*ln(M1/N1) = kT*ln(M2/N2) :: solve for N1/N2
d) N = N1 + N2 ... N2 = N/(N1/N2 + 1)
e) F = F1 + F2
F = [-N1*Δ1 - T*k*N1(ln(M1/N1)+1)] + [-N2*Δ2 - T*k*N2(ln(M2/N2)+1)]
6.3: Electrons and Holes in a Semiconductor
a) ne = nh because at T=0 they are both zero
ne = nQ*e-Δ/(2kT)
b) do the same as above but use the new temperature, then compare the ratio
c) ni=nQ*e-Δ/(2kT)
nenh=ni2 :: nh=ni2/ne
6.4: Water and Steam
a) V=m/d ... mass and density are given
b) V=nRT/p ... n = m*(1mol / .018 kg)
c) constant pressure = Isobaric
W = p*ΔV = p(Vb-Va)
d) L=Q/m :: Q=L*m
e) Q = ΔU + W :: ΔU = Q-W
NOTE ABOUT HOMEWORK B: THESE ANSWERS MAY NOT BE CORRECT. USE THEM AT YOUR OWN RISK.
HomeworkB 06
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1) When an ice cube (m = 21 g) melts, how much does its entropy change? It requires 333.9 J of heat to melt one gram of water.
dS = dQ/T = Cm/T
2) The specific heat of liquid water is 4.184 J/g-K. The latent heat of vaporization (liquid to gas) is 40.7 kJ/mol.
Define Qvap ≡ heat required to vaporize the water
Define Q0-100 ≡ heat needed to warm the water from freezing to boiling.
Calculate the ratio Qvap / Q0-100
5.4
3) One mole of H2O gas at T = 100°C occupies V = 3.06*10-2 m3 at p = 1 atm. Calculate its absolute entropy S neglecting rotation and vibration of the molecules.
S = kσ = 150
4) Assume that temperature of atmosphere is constant, and is approximately 5°C.
Define hH2O = the altitude where the water vapor partial pressure is half its value at sea level.
Define hN2 = the altitude where the nitrogen partial pressure is half its value at sea level.
Compare the two heights. Use 0°C = 273 Kelvin.
hH2O > hN2