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Question
Derive an Ideal gas equation. Mention the terms involved in it.
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Solution
According to Boyle’s law,
V ∝ `1/"P"` (at constant T and n) .…(1)
According to Charles’ law,
V ∝ T (at constant P and n) .…(2)
According to Avogadro’s law,
V ∝ n (at constant P and T) .…(3)
Combining relations (1), (2), and (3), we get
V ∝ `("nT")/"P"`
Converting this proportionality into an equation by introducing a constant of proportionality (‘R’ known as gas constant), we get
∴ V = `("nRT")/"P"`
On rearranging the above equation, we get
PV = nRT
where,
P = Pressure of gas,
V = Volume of gas,
n = number of moles of gas,
R = Gas constant,
T = Absolute temperature of gas.
This is the ideal gas equation or equation of state.
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