To answer this question, we will make use of some fundamental principles in thermodynamics. Here are the givens:
- Universal gas constant (R) = 8.314 J/(mol*K)
- Molar mass of air (M) = 0.02897 kg/mol
- Mass of air (mass) = 6 kg
- Initial volume of air (initial_volume) = 0.3 m^3
- Final volume of air (final_volume) = 0.15 m^3
- Temperature of air (temp) = 215C which is equivalent to 215 + 273.15 = 488.15 K in Kelvin scale.
The first step is to find the number of moles of air (n) using the equation:
n = mass / M = 6 kg / 0.02897 kg/mol = 207.105 moles
Now, we use the Ideal Gas Law equation P=nRT/V to figure out the initial and final pressure of the air. The Ideal Gas Law states that the pressure of a certain amount of gas is directly proportional to its temperature and volume and inversely proportional to its volume.
The pressure is calculated by the equation: P = nRT/V
First, let's calculate the initial pressure. We know the number of moles (n), universal gas constant (R), temperature (T) in Kelvin, and initial volume (V):
P_initial = nRT / initial_volume = 207.105 moles * 8.314 J/(mol*K) * 488.15 K / 0.3 m^3 = 2801849.568519158 Pa
Then we calculate the final pressure when the volume of air has reduced to final_volume:
P_final = nRT / final_volume = 207.105 moles * 8.314 J/(mol*K) * 488.15 K / 0.15 m^3 = 5603699.137038316 Pa
So, the initial pressure of the air is 2801849.568519158 Pascal (Pa)
and the final pressure of the air when it's isothermally compressed to a volume of 0.15 m^3 is 5603699.137038316 Pascal (Pa).
It's expected that the pressure would increase after the compression because the volume of the gas decreases while the temperature remains constant throughout the process.