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## Homework Statement

In a closed vessel there was some water vapor. After the water vapor dissociated, the temperature decreased by 10%, and the volume by 20%. Find the change in internal energy.

[itex](U{initial}-U{final})/U{initial}[/itex]

## Homework Equations

## The Attempt at a Solution

Let's state, that not all of water vapor dissociated. Let's say that in the beggining there was [itex]n[/itex] moles of [itex]H_2O[/itex] , and [itex]x[/itex] moles of it dissociated.

Since [itex]xH_2O -> xH_2 + 0,5xO_2[/itex] , then we get [itex]x+0,5x[/itex] moles in total of hydrogen and oxygen combined.The total moles of gas molecules after the dissociation would be [itex](n-x) + (x+0,5x)=n+0,5x[/itex]

Then i can write the ideal gas law before and after the dissociation.

[itex]pV=nRT_1[/itex]

[itex]0.8pV=0,9(n+0,5x)RT_1[/itex]

to continue, i have to find x in terms of n , but after solving the above, i get that x is a negative number. Please help !