# 6.6: Gas Law Equations: Relating the Volume and Temperature of a Gas

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The experiments that investigated how changing the temperature of a constant amount of gas impacted its volume under isobarometric, or constant-pressure, conditions were performed by a French physicist named Jacques Charles. By increasing the temperature of a gas, its constituent particles move more quickly and, therefore, collide more often with the surfaces of the container in which they are held. If the container is flexible, increasing the frequency of these collisions causes the container to expand. Therefore, the volume and temperature of a gas are *directly*, or *linearly*, proportional to one another, and dividing these quantities yields a constant, k_{3}, as shown below.

\( \dfrac{ \text{V}}{\text{T}} \) = \(\rm{k_3}\)

Like k_{1} and k_{2}, k_{3} is not a universal constant, because its value varies based on the identity of the gas that is being studied. Therefore, the most practical representation of **Charles's Law** directly relates the volume and temperature of a gas at the beginning of an experiment to their corresponding final values. This equation, which is shown below, can also be written using variables that have abbreviated or modified subscripts.

\( \dfrac{ \rm{V_{initial}}}{\rm{T_{initial}}} \) = \( \dfrac{ \rm{V_{final}}}{\rm{T_{final}}} \)

\( \dfrac{ \rm{V_{i}}}{\rm{T_{i}}} \) = \( \dfrac{ \rm{V_{f}}}{\rm{T_{f}}} \)

\( \dfrac{ \rm{V_{1}}}{\rm{T_{1}}} \) = \( \dfrac{ \rm{V_{2}}}{\rm{T_{2}}} \)