Question

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

Answer 1

Answer:

Percentage of error is 67.2%

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

$v = \frac{0.188(380)}{7\times 10^{3}}$

v = 0.01020 m^3/kg

Reduced Pressure

$P_R = \frac{P}{P_{CR}} = \frac{7}{7.39} = 0.947$

reduced temperature

$T_R = \frac{T}{T_{CR}} = \frac{380}{304.2} = 1.249$

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

$v = \frac{0.6\times 0.1889\times 380}{7\times 10^3}$

v = 0.00615 m^3/kg

percentage of error is

$= \frac{0.01020- 0.0061}{0.0061} \times 100 = 67.21$%