# How are absolute temperature and volume of a gas related?

Jan 27, 2014

The volume of a gas is directly proportional to its absolute temperature.

More specifically, for a fixed mass of gas at a constant pressure, the volume (V) is directly proportional to the absolute temperature (T). This is Charles’ Law.

V ∝ T

V = kT, where k is a proportionality constant.

$\frac{V}{T}$ = k

Since k is a constant,

(V₁)/(T₁) = (V₂)/(T₂)

EXAMPLE

A gas has a volume of 30.0 cm³ at 30 °C (303 K). What is its volume at 60 °C (333 K)?

Solution

V₁ = 30.0 cm³; T₁ = 303 K; V₂ = ?; T₂ = 333 K

(V₁)/(T₁) = (V₂)/(T₂)

V₂ = V₁× (T₂)/(T₁) = 30.0 cm³ ×$\frac{333 K}{303 K}$ = 33.0 mL

The absolute temperature increased by a factor of $\frac{330}{303}$ = 1.10, and the volume increased by the same factor: $\frac{33.0}{30.0}$ = 1.10. The volume is directly to the absolute temperature.