A 10.0-ft ³ compressed-air tank is being filled. Before the filling begins, the tank is open to the atmosphere. The reading on a Bourdon gauge mounted on the tank increases linearly from an initial value of 0.0 to 100 psi after 15 seconds. The temperature is constant at 72°F, and atmospheric pressure is 1 atm.

(a)

Calculate the rate n˙(lb-mole/s) at which air is being added to the tank, assuming ideal-gas behavior. ( Suggestion: Start by calculating how much is in the tank at t=0.)

(b)

Let N(t) equal the number of lb-moles of air in the tank at any time. Write a differential balance on the air in the tank in terms of N and provide an initial condition.

(c)

Integrate the balance to obtain an expression for N(t). Check your solution two ways.

(d)

Estimate the lb-moles of oxygen in the tank after two minutes. List reasons your answer might be inaccurate, assuming there are no mistakes in your calculation.