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Chemistry

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 ?

Gas Laws

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Answer

Initial conditions:

V1 = Initial volume of the gas = V
T1 = Initial temperature of the gas = ?

Final conditions

V2 (Final volume) = reduce by 20%

= V - 20100\dfrac{20}{100} of V

= 80V100\dfrac{80\text{V}}{100}

= 4V5\dfrac{4\text{V}}{5}

T2 = Final temperature of the gas = 157°C = 157 + 273 = 430 K

By Charles Law:

V1T1=V2T2\dfrac{\text{V}1}{\text{T}1} = \dfrac{\text{V}2}{\text{T}2}

Substituting the values :

VT1=4V54301T1=45×430T1=430×54T1=537.5K\dfrac{\text{V}}{\text{T}1} = \dfrac{\dfrac{4\text{V}}{5}}{430} \\[1em] \dfrac{\text{1}}{\text{T}1} = \dfrac{4}{5 \times 430} \\[1em] \text{T}1= \dfrac{430 \times 5}{4} \\[1em] \text{T}1 = 537.5 \text{K}

Therefore, final temperature of the gas = 537.5 K - 273 K = 264.5°C

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