1. The problem statement, all variables and given/known data 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 3. 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.