The Combined Gas Law
Combined Gas Law defined & explained; practical applications for building air conditioning, heat pumps, oil storage tanks, water pressure tanks, LP & natural gas systems
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
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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