A finance lesson from the behaviour of gases under pressure!

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

06 November 2016

Studying the physical properties of gases is a very trick affair. Even though there are only three parameters to deal with, namely, volume, pressure and temperature, the challenge is that changing one affects the values of the others.

When a gas is compressed (pressure increased), its volume decreases and its temperature rises. We observe this when pumping a bicycle tyre – the pump warms up.

For many centuries, scientists tried to understand the relationship between these three parameters – volume, temperature and pressure. The first crack in the puzzle appeared in the year 1622 when Robert Boyle discovered (experimentally) that, if the temperature is held constant, then the volume is inversely proportional to pressure.

This means that if you increase the pressure by, say 20 per cent, the volume will decrease by the same proportion, 20 per cent. It is surprising that, even after Boyle had discovered the trick behind the puzzle (holding one of the parameters constant), it took another 165 years before the next law was found.

In 1787, Jacques Charles discovered (also experimentally) that if the pressure is held constant, the volume of a gas is directly proportional to it is “absolute temperature”. Charles’s stroke of genius was the introduction of the concept of an “absolute temperature” scale – its values are not degrees; they are just plain numbers!

Still, another two decades passed before the third law was discovered by Joseph Gay-Lussac in 1809. He found that, if the volume is held constant, then the pressure is directly proportional to the absolute temperature.

177 years to discover three simple laws? I still can’t get over that!

I was reminded about these events by an email conversation that I had with Mr. Kimathi Mwirichia. He wrote in to challenge the statement I made in last week’s article that “the monthly instalment of a loan is not directly proportional to the interest rate”.

He argued that, if the rate changes from 20 per cent to 14.5 per cent, then the instalment on a Sh1,000,000 loan can change from the initial Sh26,494 to Sh19,188 if the term is changed from 60 to 83 months. He goes on to demonstrate that the change from Sh26,494 to Sh19,188 is directly proportional to that from 20 to 14.5 per cent.

My response was that you can’t change two parameters simultaneously. Just like in the case of the gas laws, you must hold one factor constant and the then study the other two. However, Mwirichia does not agree with me. Not even after I presented him with the mathematical equations used in the calculations.

He suggested that “we involve independent professionals and intellectuals in the field to vouch the veracity of my [Mwirichia’s] critical analysis”. I have taken up the challenge and posted the chain of emails HERE. I invite readers to read them and help us unlock the deadlock. I would especially like to hear from finance professionals.