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Here is how I would do the puzzle about barometer:

PV = nRT; n = m/M

PV = mRT/M; V = m/(rho)

p*m/(rho) = mRT/M

p/(rho) = RT/M

(rho) = pM/RT

p + (dp) = p + (rho)g(dh)

(dp) = (rho)g(dh)

(dp) = pMg(dh)/RT

(dp)/p = Mg(dh)/RT

integrate 0 to p (dp)/p = integrate h to 0 [Mg(dh)/RT]

ln(p) = -Mgh/RT + c

take h = 0 at bottom of building, then

ln(p_at_h=0) = c => read c from barometer to get constant

now, at height h we will read p_at_h=height from barometer, then:

ln(p_at_h=height) = -Mgh/RT + ln(p_at_h=0)

Mgh/RT = -ln(p_at_h=height) + ln(p_at_h=0)

Mgh = -RTln(p_at_h=height) + RTln(p_at_h=0)

-----------------------------------------------------------------------------

| height = -RTln(p_at_h=height)/Mg + RTln(p_at_h=0)/Mg =

| = RT/Mg(ln(p_at_h=0) - ln(p_at_h=height)) =

| = RT/Mg(ln(p_at_h=0/p_at_h=height))

-----------------------------------------------------------------------------

p in Pascals

g = 9.81

R = 8.31

T = temperature in absolute units

M = 28.97

I hope i did it right ;)




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