Question

4. Beginning with PV = nRT, derive ρ = PM/(RT). Note M = molecular weight and m = mass.
5. Derive p2=p1exp(-gMdeltaZ/Rt) for an isothermal, perfect gas.
6. List the equations for pressure and temperature of an isentropic perfect gas.

Answer 1

Question 1

PV=nRT

(n=w/M)

P= wRT/VM (w/V=ρ )

P= ρRT/M

ρ= PM/RT

Question 2

From hydrostatic equation

dp+ ρgdZ = 0 (putting value of ρ= PM/RT)

$\frac{dp}{p}$ + $\frac{gM dZ}{RT}$ = 0

$\frac{P2}{P1}$ = exp( $\frac{-gM(z2- z1)}{RT}$ )