Question 7.14: Problem: Calculate the specific volume of steam at a tempera...
Problem: Calculate the specific volume of steam at a temperature of 600 °C and pressure of 10 MPa using (a) steam tables, (b) the ideal gas equation and (c) the generalised compressibility charts.
Find: Specific volume of steam ν.
Known: Temperature T = 600 °C = 873.15 K, pressure P = 10 MPa.
Governing Equations:
Ideal gas equation Pν=RT
Compressibility factor Z=\frac{Pν}{R_uT}
Properties: For water, gas constant R = 0.4615 kJ / kgK (Appendix 1), critical temperature T_C = 647.3 K and critical pressure P_C = 22.09 MPa (Table 7.1).
| Table 7.1 Critical temperature (T_c), pressure (P_c) and volume (v_c) of common substances. | ||||
| Substance | Formula | Temperature, T_c (K) | Pressure, P_c (MPa) | Volume, v̄_c (m^3 /kmol) |
| Air | — | 132.5 | 3.77 | 0.0883 |
| Ammonia | NH_3 | 405.5 | 11.28 | 0.0724 |
| Argon | Ar | 151 | 4.86 | 0.0749 |
| Carbon dioxide | CO_2 | 304.2 | 7.39 | 0.0943 |
| Helium | He | 5.3 | 0.23 | 0.0578 |
| Methane | CH_4 | 191.1 | 4.64 | 0.0993 |
| Nitrogen | N_2 | 126.2 | 3.39 | 0.0899 |
| Oxygen | O_2 | 154.8 | 5.08 | 0.078 |
| Water | H_2O | 647.3 | 22.09 | 0.0568 |
(a) From the superheated steam tables (Appendix 8c) at T = 600 °C and P = 10 MPa, specific volume ν = 0.038 37 kg / m³.
(b) From the ideal gas equation,
\nu = \frac{RT}{P}=\frac{0.4615 \times 10^3 \ J/kgK \times 873.15 \ K}{10 \times 10^6 \ Pa}= 0.040 \ 296 \ m^3/kg.
(c) Using the generalised compressibility charts (Appendix 10), with reduced temperature
T_r= \frac{T}{T_c}=\frac{873.15 \ K}{647.3 \ K} =1.348 \ 95 =1.35
and reduced pressure
P_r= \frac{P}{P_c}= \frac{10 \ MPa}{22.09 \ MPa} = 0.452 \ 69=0.45,
then the compressibility factor Z = 0.95.
P=Z\frac{RT}{P}=0.95 \times \frac{0.4615 \times 10^3 \ J/kgK \times 873.15 \ K}{10 \times 10^6 \ Pa}=0.038 \ 281 m^3/kg.
Answer: The specific volume calculated using (a) superheated steam tables is 0.0384 kg / m³ , (b) ideal gas equation is 0.0403 kg / m³ and (c) generalised compressibility charts is 0.0383 kg / m³.