on August 9th, 2012

Dear Colleagues

An interesting little (simple) brain teaser for you – no matter whether what discipline or type of engineering professional you are.

The Challenge
A tank at atmospheric pressure contains 1 kg of air. The tank is then pressurized with an additional 3 kgs of air. What is the resultant gauge pressure (in bars) in the tank after this 3kgs of air has been added? Absolute pressure = gauge pressure + atmospheric pressure

A. 1 bar
B. 3 bar
C. 4 bar

You could use the Universal Gas Law in your deliberations:

PV = nRT

Where V is volume; P is absolute pressure; n is the number of moles (‘molecules’); R is a constant and T is the temperature.

Assume atmospheric pressure is 1 bar (the initial pressure) – naturally this is a number which could change depending on what altitude you are at.

Solution (suggested – you could do it in a myriad of different ways)
There is initially 1kg of air occupying V0 initial volume.

With 3kgs of air added; there is now a total of 4kg of air in the tank (thus the final number of moles or particles is effectively 4 times that of the initial number).

The volume (V0) and temperature (TO) of the tank still stays the same.

Thus:

P0 V0  = n0 R T0 (initial state)
P1  V0  =  n1 R T0  (final state where n1 = 4 x n0)
Thus – dividing each side of equation 1 and 2 we get:

P1  V0 / P0 V0  =  4 x n0 R T0  /  n0 R T0

P1  V0 / P0 V0  =  4 x n0 R T0  /  n0 R T0

Thus P1 = 4 P0

Hence, the final pressure P1 = 4 bar absolute or 3 bar gauge pressure (thus answer B above)

Do you agree?

My humble appreciation to Dr Rodney Jacobs and David Spitzer (the flow guru) for their contributions and critique.

Albert Einstein remarked: I never teach my pupils. I only attempt to provide the conditions in which they can learn.

Yours in engineering learning

Steve


      

The latest news

EIT Research: How to Construct Quake-Resistant Buildings

EIT Research: How to Construct Quake-Resistant Buildings

EIT Research: A recent catastrophic earthquake in North Africa that claimed thousands of lives has caused civil and environmental engineering experts to emphasize the need for quake-proof buildings. Read on...... Read more
Engineering Standards: What are They and Why They Matter?

Engineering Standards: What are They and Why They Matter?

Engineering standards are an essential part of the modern engineering landscape, guiding everything from product design to manufacturing processes and safety procedures. These standards, which are developed and maintained by...... Read more
The Harsh Realities of Job Security for Engineers

The Harsh Realities of Job Security for Engineers

Job security is a major consideration for anyone, and engineering is often regarded as one of the most secure fields. But how secure is it, really? In this article, we...... Read more
EIT - South Africa