Question

Derive an Ideal gas equation. Mention the terms involved in it.

Answer 1

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.