Answer to Question #278421 in Molecular Physics | Thermodynamics for Neilmar

Question

Find the density of air at 13.79 MPaa and 172.8 K, using (a) pv = RT, (5) pv = ZRT, (c) van der Waals equation. (d) Which of the three answers do you believe is more accurate?

Answer 1

PV= RT

$V=\frac{RT}{P}$

$V=\frac{8.31\times172.8}{13.79\times10^6}$

$V=1.041\times10^{-4}m^3$

Now

$PV=RT$

$$13.79\times1.041\times10^{-4}={8.31\times172.8}$$

LHS=RHS

(2)

$Z=\frac{PV}{RT}$

$Z=\frac{13.79\times10^6\times1.041\times10^{-4}}{8.31\times172.8}=0.99$

PV=ZRT

LHS=RHS

(3)

Vander Wal equation

$(P-\frac{an^2}{V^2})(V-nb)=nRT$

$$(13.79\times10^6-\frac{a}{1.014\times10^{-4}})(1.014\times10^{-4}-b)=1\times8.321 \times172.8$$

LHS=RHS