NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.

A tank with an internal volume of 1 m³ contains air at 800 kPa and 25C. A valve on the tank is opened, allowing air to escape, and the pressure inside quickly drops to 165 kPa, at which point the valve is closed. Assume there is negligible heat transfer from the tank to the air left in the tank. The gas constant of air is 0.287 kPam³/kgK. The specific heats of air at room temperature are c_P = l.005 kJ/kgK and c_v = 0.718 kJ/kgK. Also k = 1.4.

Using the approximation h_e constant = h_{e, avg} = 0.5(h₁ + h₂), calculate the mass withdrawn during the process.

The mass withdrawn during the process is ____ kg.

Consider the same process but broken into two parts. That is, consider an intermediate state at P₂ = 400 kPa, calculate the mass removed during the process from P₁ = 800 kPa to P₂ and then the mass removed during the process from P₂ to P₃ = 165 kPa, using the type of approximation used in part (a), and add the two to get the total mass removed.

The total mass withdrawn is ____ kg.

Calculate the mass removed if the variation of h_e is accounted for.

The mass withdrawn is _____kg.