Final answer:
The mass of the air in the tank can be determined using the ideal gas law equation, which relates the pressure, volume, and temperature of a gas to its mass. In this case, the mass of the air is approximately 383.6 kg.
Step-by-step explanation:
The mass of the air can be determined using the ideal gas law equation, which relates the pressure, volume, and temperature of a gas to its mass. The ideal gas law equation is:
pV = mRT
Where:
- p is the pressure of the gas
- V is the volume of the gas
- m is the mass of the gas
- R is the ideal gas constant
- T is the temperature of the gas in Kelvin
In this question, the volume is given as 2 m³, the pressure is given as 1.4 MPa, and the temperature is given as -93°C. To convert the temperature to Kelvin, we add 273.15:
T = -93 + 273.15 = 180.15 K
Plugging these values into the equation:
1.4 MPa * 2 m³ = m * R * 180.15 K
Now, we need to convert the pressure from MPa to Pa and the volume from m³ to L:
1.4 MPa = 1.4 * 10^6 Pa
2 m³ = 2 * 10³ L
Substituting these values into the equation:
1.4 * 10^6 Pa * 2 * 10³ L = m * R * 180.15 K
Simplifying:
2.8 * 10^6 * 10³ = m * R * 180.15
Dividing both sides by the ideal gas constant R, which has a value of 8.314 J/(mol·K):
m = (2.8 * 10^6 * 10³) / (8.314 * 180.15) kg
Calculating this value:
m ≈ 383.6 kg