JEE Main & Advanced Physics Thermometry, Calorimetry & Thermal Expansion Expansion of Gases

Gases have no definite shape, therefore gases have only volume expansion. Since the expansion of container is negligible in comparison to the gases, therefore gases have only real expansion.

(1) Coefficient of volume expansion : At constant pressure, the unit volume of a given mass of a gas, increases with \[{{1}^{o}}C\] rise of temperature, is called coefficient of volume expansion.

\[\alpha =\frac{\Delta V}{{{V}_{0}}}\times \frac{1}{\Delta \theta }\]\[\Rightarrow \]Final volume \[{V}'=V(1+\alpha \Delta \theta )\]

(2) Coefficient of pressure expansion : \[\beta =\frac{\Delta P}{P}\times \frac{1}{\Delta \theta }\]  

\[\therefore \] Final pressure \[{P}'=P(1+\beta \Delta \theta )\]

For an ideal gas, coefficient of volume expansion is equal to the coefficient of pressure expansion i.e. \[\alpha =\beta =\frac{1}{273}{}^\circ {{C}^{-1}}\]