Gaseous State | Gas Laws#
Boyle's Law#
- At constant temperature, the pressure of a fixed mass of a gas is inversely proportional to its volume.
\[P ∝ {1 \over V}\]
\[PV = constant\]
Charle's Law#
- At constant pressure, the volume of a fixed mass of a gas is directly proportional to its temperature.
\[V ∝ T\]
\[ {V \over T} = constant\]
where, T = Absolute Temperature (Kelvin scale)
\[Slope, m = tan Θ = {V_0 \over 273.15} ≈ {V_0 \over 273}\]
\[∴ V = {V_0 \over 273}T + V_0\]
where, T is in celsius.
- A new temperature scale was introduced known as Kelvin scale.
Gay Lussac's Law#
- At constant volume, for a fixed mass of a gas, pressure is directly proportional to its temperature.
\[P ∝ T\]
\[ {T \over P} = constant \]
where, T = Absolute Temperature (Kelvin scale)
Note
Mean free path, \(λ ∝ {T \over P}\). If Gay Lussac's Law is valid or applicable, then mean free path is constant. We will discuss mean free path in detail later.
Avogadro's Hypothesis#
-
At constant temperature and pressure, volume occupied by a gas, V is directly proportional to its number of moles, n.
-
More accurately, if \({T \over P} = constant\), then:
\[V ∝ n\]