How to calculate temperature of expanded ideal gas.

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How to calculate temperature of expanded ideal gas.

By definition an ideal gas in a closed follows the relationship of PV=nRT, or PV/T = constant

This means that Pressure * Volume/ Temperature will be the same at the start and end of the process.

So P₁V₁/T₁=P₂V₂/T₂

Assuming that we have a gas at a temperature of 300k (T₁) in a piston initially at 1m³(V₁) which is then expanded at constant pressure (isobaric) to 2m³.(V₂) What would be the final temperature?

As Pressure is the same at the start and end of the process, we can ignore the pressure terms, giving

V₁/T₁=V₂/T₂

Rearranging the equation to give a solution to T₂

T₂=V1*T₁/V2

Thus filling in the terms we already know, gives

T₂=1*300/2

T₂=150k

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