IDEAL AND REAL GASES 405

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\M-therm\Th8-2.pm5

Example 8.13. Calculate the density of N 2 at 260 bar and 15°C by using the compressibility

chart.

Solution. Pressure, p = 260 bar

Temperature, T = 15 + 273 = 288 K

Density, ρ =?

For N 2 (from Table 8.3) : pc = 33.94 bar

Tc = 126.2 K

Now pr =

p

pc =

260

33 94.

= 7.6

and Tr =

T

Tc =

288

126 2.

= 2.28

From the compressibility chart for pr = 7.6 and Tr = 2.28, Z (^) ~− 1.08
Also Z =
pv
RT =
p
ρRT , where ρ stands for density
or ρρρρρ = p
ZRT

260 10
108 8314
28
288
×^5

. ××

= 281.5 kg/m^3. (Ans.)

Example 8.14. What should be the temperature of 1.3 kg of CO 2 gas in a container

at a pressure of 200 bar to behave as an ideal?

Solution. Pressure, p = 200 bar

Temperature, T =?

For CO 2 (from Table 8.3) pc = 73.86 bar

Tc = 304.2 K

As the gas behaves like an ideal gas, Z = 1

pr = p

pc

=^200

73 86.

= 2.7

From compressibility chart for Z = 1, pr = 2.7

Tr = 2.48

∴ T = Tr × Tc = 2.48 × 304.2 = 754.4 K. (Ans.)

Example 8.15. A spherical shaped balloon of 12 m diameter contains H 2 at 30°C and

1.21 bar. Find the mass of H 2 in the balloon using real gas equation.

Solution. Diameter of spherical balloon = 12 m

∴ Volume, V = 4/3 π × (6)^3 = 904.78 m^3

Temperature, T = 30 + 273 = 303 K

Pressure, p = 1.21 bar

Mass of H 2 in the balloon, m :

For H 2 (from Table 8.3) pc = 12.97 bar

Tc = 33.3 K

Now, pr = p

pc

=^121

12 97

.

.

= 0.093

Tr =

T

Tc

=

303

33 3.

= 9.1

~−