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Suppose you are holding a container of gas, and the container has a fixed volume (i.e. it won't stretch or give to allow for expansion or contraction). if the gas pressure in the container has doubled while you were holding it, then what must have happened to the temperature?

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Edufirst

Answer: if the pressure in the container is doubled, then the temperature will double too.


Justification:


You can rely on Gay-Lussac's law for ideal gases to answer the question.


According to that law, the pressure and temperature of a fixed amount of gas in a closed rigid container (constant volume) varie in direct proportion.


Mathematically, you can write in this way:


P/T = k


P₁ / T₁ = P₂ / T₂


That means, that if the pressure in the container is doubled, then the temperature will double too.


You can see that mathematically:


P₂ = 2 P₁


T₂ = (T₁ / P₁)(P₂) = (T₁ / P₁) (2 P₁) = 2 T₁

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