Question

What is the percentage of error involved in treating carbon dioxide at 7 MPa and 380 K as an ideal gas?

Answer 1

Percentage of error is 67.2%

Step-by-step explanation:

from table A-1 of thermodynamics " gas constant and critical point properties" obtain CO_2 properties

from table

critical temperature
`T_(CR) = 304.2 k`

critical pressure
`P_(cr) = 7.39 MPa`

Gas constant R = 0.188 kJ/kg -K

From ideal gas equation we have

PV = RT

solving of v we have

`v = (0.188(380))/(7* 10^(3))`

v = 0.01020 m^3/kg

Reduced Pressure

`P_R = (P)/(P_(CR)) = (7)/(7.39) = 0.947`

reduced temperature

`T_R = (T)/(T_(CR)) = (380)/(304.2) = 1.249`

obtained compressibility factor (z) from chart between reduced temperature and reduced pressure.

from
`P_R = 0.947 and T_R = 1.249, Z value is 0.6`

so we have

Pv = ZRT

`v = (0.6* 0.1889* 380)/(7* 10^3)`

v = 0.00615 m^3/kg

percentage of error is

`= (0.01020- 0.0061)/(0.0061) * 100 = 67.21`%