How do you derive the Ideal Gas Law from Boyle and Charles’ laws?
Boyle’s law says that PV = constant, provided temperature (T) is constant.
Charles’ law says that V/T = constant, provided that pressure (P) is constant.
The problem is: my physics and chemistry textbooks then declare that “combining the two laws together, you get VP/T = constant (the ideal gas law). But they never bother to explain exactly how it is derived from those two. Does anyone know how the two are combined to get it?
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Applying Boyle's law, at constant temperature the volume of a gas varies inversely to the pressure.
V proportional to 1/P
Applying Charles' law, at constant pressure the volume of gas varies directly to the temperature.
V proportional to T
Combining the two laws, the volume of the gas is inversely proportional to pressure and directly proportional to temperature.
(If ~ is used as the symbol for proportionality)
V ~ 1/P
V ~ T
A constant (k) is introduced to remove the proportionality sign.
Hence, combining the two laws,
V = K * T/P
which implies that
VP/T = K = constant