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Question
It is required to reduce the volume of a gas by 20% by compressing it at a constant pressure. To do so, the gas has to be cooled. If the gas attains a final temperature of 157°C, find the initial temperature of the gas.
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Solution
Initial conditions:
V1 = Initial volume of the gas = V
T1 = Initial temperature of the gas = ?
Final conditions:
V2 (Final volume) = reduce by 20%
= V - `20/100` of V
= `(80"V")/100`
= `(4"V")/5`
T2 = Final temperature of the gas = 157°C = 157 + 273 = 430 K
By Charles Law:
`"V"_1/"T"_1 = "V"_2/"T"_2`
Substituting the values:
`"V"/"T"_1 = ((4"V")/5)/430`
`1/"T"_1 = 4/(5 xx 430)`
T1 = `(430 xx 5)/4`
T1 = 537.5 K
Therefore, final temperature of the gas = 537.5 K - 273 K = 264.5°C
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