David W. Spitzer

A tank at atmospheric pressure contains 1 kg of air. The tank is pressurized with 2 kg of additional air. What is the pressure in the tank after the 2 kg of air is added?
A. 2 bar
B. 3 bar
C. 4 bar
D. 5 bar

Commentary
For flow measurement purposes, Boyle”s Law is often used to calculate the change in volume that occurs when pressure changes:

V / V0 = P0 / P

where V is volume and P is the absolute pressure. In this problem, 1 kg of air initially occupies the entire volume of the tank (V0). There are 3 kg of air in the tank after it is pressurized with the additional air. Therefore, 1 kg of air now occupies only one-third of the tank volume. Estimating atmospheric pressure to be 1 bar (for ease of calculation), substituting into the above equation (where p is gauge pressure), and solving for p yields:

(1/3 V) / V = 1 / (p +1)
p = 2 bar

Therefore, the correct answer is Answer A.

Additional Complicating Factors
It is good practice to check the answer. A pressure of 2 bar gauge is an absolute pressure of 3 bar absolute. Boyle”s Law states that the volume of an ideal gas is inversely proportional to its absolute pressure, so air at 3 bar absolute pressure will occupy one-third of the volume that it occupies at 1 bar absolute pressure. Therefore, the air that originally filled the tank will now occupy one-third of the tank and the additional air will occupy the remaining two-thirds of the tank.

David W. Spitzer
is a regular contributor to Flow Control with more than 35 years of experience in specifying, building, installing, startup, troubleshooting, and teaching process control instrumentation. Mr. Spitzer has written over 10 books and 150 technical articles about instrumentation and process control, including the popular “Consumer Guide” series that compares flowmeters by supplier. Mr. Spitzer is a principal in Spitzer and Boyes LLC, offering engineering, expert witness, development, marketing, and distribution consulting for manufacturing and automation companies. He can be reached at 845 623-1830.