Chapter 10, Problem 10.4P

Interpretation Introduction

(a)

Interpretation:

Before a Compressed air tank of 10.0 ft³begins to fill, it is open to the atmosphere.Bourdon Pressure gauge reading mounted on tank increases linearly from initial value 0to 100 psi after 15 seconds. Temperature is 72 °F and Atmospheric Pressure is 1atm.What is the rate at which air is being added to the tank (lb-mole/s)

Concept introduction:

Assume Ideal gas behaviour:

At higher temperature and pressure a gas behaves as an ideal gas, if as compare to particles kinetic enery, the potential energy due to intermolecular forces become less.

And also compare to the size of empty space between molecules become less.

Interpretation Introduction

(b)

Interpretation:

Differential balance in the air on tank in form of N and give initial condition.

Concept introduction:

Assume N(t) equal the number of lb-mole of air in tank at any time.

$\begin{array}{l}PV=nRT\hfill \\ N\alpha P\hfill \end{array}$

Interpretation Introduction

(c)

Interpretation:

Expression for N(t)

Concept introduction:

Integration method

Integration method is used to find integral. Integration method involves the power of trigonometric functions.

Interpretation Introduction

(d)

Interpretation:

Lb moles of oxygen in the tank

Concept introduction:

Molecular weight of oxygen is 32 lb/mole at critical temperature of -181.8 F and the critical pressure of 729.1 psia.