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

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.

##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 ×##(333 K)/(303 K)## = 33.0 mL

The absolute temperature increased by a factor of ##330/303## = 1.10, and the volume increased by the same factor: ##33.0/30.0## = 1.10. The volume is directly to the absolute temperature.