What is the final temperature inside the vessel after combustion?

[YoChem]

Homework Statement

An empty 4 L steel vessel is filled with 1 atm of CH4 and 4 atm of O2 at 300K. A spark causes the following reaction totake place.
CH4 + O2 ------> CO2 + 2H20 delta H=-802 kj

What is the final temperature inside the vessel after combustion assuming that the steel vessel has a mass of 14.5 kg, the mixture of the gases have an average molar heat capacity of 21 J/mol C and the heat capacity of steel is .449 J/g C

Homework Equations

Heat evolved = Specific Heat * Mass * Delta T

The Attempt at a Solution

I tried substituting the information from the problem into the above equation, once for the gas and once for the steel, then adding the two number together, but it isn't working out so much.
I know the answer is 310 C.
Cheers in advance.

 

[Borek]

You are probably not completely off. In both heats you calculated delta T is identical. Sum of both heats quals heat evolved while burning the gas. That should be enough to write equation and solve for delta T.

 

[morrobay]

Are you sure about that 310 C answer ?

Setting the delta Temps equal, I have:

802000 J - x J / (.449 J/g C ) (14500 g ) = x J /(.787 J/g C ) (80g) *
x = 7682 J
794318 J /6510.5 J C = 7682 J / 63 J C
122 C = 122 C = delta T

* I converted the 21 J / mole C for the three gases : 63 J /80g C = .787 J /g C