Final answer:
To calculate the specific volume of air acting as an ideal gas, the ideal gas law PV = nRT is used, adjusting it for specific volume as V = RT/P. The given gas constant for air is then used along with the provided temperature and pressure values to find the specific volume in m³/kg. Therefore, the specific volume of air under these conditions would be approximately 85.546 m³/kg.
Step-by-step explanation:
To calculate the specific volume of air acting as an ideal gas, given its pressure in MPa, temperature in K, and the gas constant for air in kJ/(kg K), you can use the ideal gas law, which is expressed as PV = nRT. Firstly, note that we must ensure all units are consistent, typically converting pressure into kPa to match the unit of the gas constant. Since we are looking for the specific volume (volume per unit mass), we need to adjust the ideal gas law to V = RT/P, where V is the specific volume, R is the gas constant, T is the absolute temperature, and P is the pressure. In the case of air, the gas constant (R) is typically about 0.287 kJ/(kg K) or 287 J/(kg K) when converting from kJ to J (since 1 kJ = 1000 J).
For example, if the pressure P is given as 1 MPa (which is 1000 kPa), and the temperature T is 298 K, then the specific volume V would be calculated as follows:
V = RT/P
V = (287 J/(kg K)) * (298 K) / (1000 kPa) = (287 * 298) / 1000 m³/kg
V = 85546 / 1000 m³/kg
V ≈ 85.546 m³/kg
Therefore, the specific volume of air under these conditions would be approximately 85.546 m³/kg.