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Charle's Law ... V ∝ f(T); Pressure and Mass remain constant

Explanation:

Charle's Law is one of the empirical gas laws relating the effect of temperature on volume of a gas while pressure and mass (moles) of substance remain constant. Basically, Charle's Law states that the change in volume associated with a confined mass or gas is directly proportional to the applied temperature.

For a directly proportional relationship between Volume (V) and Temperature (T) the empirical formula is written V ∝ T. This is then set in equation form by including a 'proportionality constant' giving V = k·T. In applications, problems generally provide 'initial' Temperature (T₁) and Volume (V₁) along with a final Temperature (T₂) or final Volume (V₂) and asked to calculate the unknown variable. The Charle's Law relationship detailing this is derived as follows:

V = k·T => k = V/T

The k-value is constant for both the initial and final conditions such that...

k₁ = k₂ => V₁/T₁ = V₂/T₂

Example: Assume a gas volume of 25 liters at 25°C, what would be the gas volume if cooled to 0°C?

Set-up a data table

V₁ = 25L     & V₂ = ?

T₁ = 25°C   & T₂ = 0°C => these values need to be converted to Kelvin Temps so as to avoid division by '0'. So...

T₁ = (25 + 273)K = 298K     &     T₂ = (0 + 273)K = 273K

Substituting into V₁/T₁ = V₂/T₂ and solving for V₂ provides the new volume.

25L/298K = V₂/273K => V₂ = (25L)(273K)/(298K) = 22.9L ≅ 23L (2 sig. figs.)

Generally, to check work, examine the change in volume relative to the change in temperature. For a direct proportionality a decrease in temperature as in the example would give a decrease in volume consistent with Charle's Law. Note that 273K/298K  times  25L gives a smaller resulting volume value. If one applies '298K/273K' times the 25L,  a larger value would result and is inconsistent with Charle's Law.  

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