# The Combined Gas LawCombined Gas Law defined & explained; practical applications for building air conditioning, heat pumps, oil storage tanks, water pressure tanks, LP & natural gas systems       (function() { var po = document.createElement('script'); po.type = 'text/javascript'; po.async = true; po.src = 'https://apis.google.com/js/platform.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(po, s); })();

• COMBINED GAS LAW - CONTENTS: definition of Boyle's Law with examples of using Boyle's Law to explain what happens to air in a water storage tank, LP gas in a gas tank, oil & fumes in an oil storage tank, or air conditioning /heat pump refrigerant liquid & gas volumes inside of an air conditioning or heat pump system.
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The Combined Gas Law: this article describes and defines the Combined Gas Law with examples of using the Combined Gas Law to join the effects of pressure, temperature, and initial volume to explain what happens to air in a water storage tank, LP gas in a gas tank, oil & fumes in an oil storage tank, or air conditioning /heat pump refrigerant liquid & gas volumes inside of an air conditioning or heat pump system.

## Definition & Practical Applications of the Combined Gas Law

The Combined Gas Law combines the effects of Boyle's Law and Charles Law thus considering gas pressure, gas volume, and gas temperature all together. The Combined Gas Law is written as

P1V1/T1 = P2V2/T2

where

P = Pressure of the gas

V = Volume occupied by the gas

T = Temperature of the gas

### Example of using the Combined Gas Law to Explain What Happens Inside of a Water Pressure Tank

But inside of our water tank the total space available for air is fixed by the physical size of the tank itself. If we're talking about air inside a water tank, the volume taken up by the air can't get bigger than the tank itself. Charles and Boyle considered individually don't tell us what happens to the air pressure and volume inside of a water tank as temperatures change.

To figure this out we need to look at pressure and temperature simultaneously using the
Combined Gas Law:   P1V1/T1 = P2V2/T2  along with some simple algebra. I'm slow at math so we have to show every step in the calculation before I'll believe it.

• Starting Formula: (33 psi X 4 cu. ft.) / 60degF = (NEWPSI X 4 cu. ft.) / 90degF
• Before using these temperatures with the gas laws they must be converted to Kelvins. The formulas for these conversions between Kelvin and Fahrenheit or Centigrade are given just above where we introduced Charle's Law. (Note 1 below).
Convert our starting temperature 60 degF to Kelvins: K1 = (60 degF + 460)/1.8 = 288 degK
Convert our ending temperature 90 degF to Kelvins: K2 = (90 degF + 460)/1.8 = 305 degK
• Corrected Combined Gas Law Formula: (33 psi X 4 cu. ft.) / 288 degK = (NEWPSI x 4 cu. ft.) / 305 degK
• 132 / 288 = (NEWPSI x 4) / 305
• .46 = (NEWPSI x 4) / 305
• .46 x 305 = NEWPSI x 4
• 140 = NEWPSI x 4
• 140/4 = NEWPSI
• 35 = NEWPSI - so we went from 33 psi to 35 psi when we increased the temperature of the air in the tank from 60 degF. to 90 degF.
• (35-33)/33 = .06 or in other words, we see about a 6% increase in pressure in the water tank when the temperature changes from 60 degF. to 90 deg.F.

One would conclude from this calculation that the effects of normal temperature changes in the environment of a water pressure tank will not have a significant effect on the in-tank pressure.

Note 1: A thoughtful reader pointed out that the measurement of temperature in these basic formulas must be counted from absolute zero, (-273 degrees Centigrade / -460 degrees Fahrenheit). Our references for Charle's Law confirm this requirement. Another simpler calculation of the effects of temperature change on water pressure tank internal pressures was suggested by Mr. Pryor. The difference between the starting and ending temperatures in degF. is divided by the starting temperature converted to Kelvins: a temperature change from 60 degF to 90 degF is (90-60)/(460+60) = 5.77% which is indeed only a small increase in pressure inside the water tank.

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