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## Homework Statement

Given the temperature of an ideal gas in a tub where it varies linearly from (x=0) to (x=L)

T = To + [(TL - To)/L]x

where To is temperature at 0 length and TL is the temperature at the end of the tube

We are suppose to show that the equation of state for this ideal gas is

PV=nR[(TL-To)/ln(TL/To)]

As well as if then To = TL = T show that the equation of state reduces to the obvious one...PV=nRT

## The Attempt at a Solution

So first off I wasnt sure of where to start because I know the only changing variable in this question is temperature so I know we are suppose to rearrange this equation

T = To + [(TL - To)/L]x

However I'm not sure on how to derive this equation.

Mostly this is alegbra/dervatives/integration problem.

And I'm honestly stuck as to where to go from the temperature equation

Any suggestions on where to begin would be greatly appreciative.