A 10.0-ft3 compressed-air tank is being filled. Before the
Chapter 11, Problem 11.4(choose chapter or problem)
A \(10.0-\mathrm{ft}^{3}\) 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 \(72^{\circ} \mathrm{F}\), and atmospheric pressure is 1 atm.
(a) Calculate the rate \(\dot{n}(\mathrm{lb}-\mathrm{mole} / \mathrm{s})\) 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 number of lb-moles of oxygen in the tank after two minutes.
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