Final answer:
To find the temperature of a gas mixture of oxygen and helium in a one cubic meter container with a pressure of 280 kPa, we use the ideal gas law formula with the given moles of each gas and solve for temperature in Kelvin.
Step-by-step explanation:
The student's question pertains to finding the temperature of a mixture of gases (oxygen and helium) in a one cubic meter container with a given pressure of 280 kPa. To solve this, we will use the ideal gas law equation PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature.
First, we need to calculate the total number of moles of gas in the mixture. Since 1 kilogram-mole (kgmol) is equivalent to 1000 moles, the total moles (n) is 0.04 kgmol × 1000 moles/kgmol + 0.06 kgmol × 1000 moles/kgmol = 40 moles + 60 moles = 100 moles. The pressure (P) is given as 280 kPa, which equals 280,000 Pa. The volume (V) is one cubic meter. The ideal gas constant (R) is 8.3145 J/(mol·K).
We can rearrange the ideal gas law to solve for temperature (T):
T = (PV) / (nR)
Substituting the known values gives us:
T = (280,000 Pa × 1 m3) / (100 moles × 8.3145 J/(mol·K))
After calculations, we would find the temperature T in Kelvin. This equation helps in understanding the properties of gas mixtures and their behavior under different conditions.