hmm,
To solve this problem you have to look at it in a qualitative way at first, then when you understand whats happening then and only then put the numbers in the equations, makes doing the problem a lot easier, and you probably get the right answer.
1. heat is evolved from the combustion of acetylene
2. which goes into the surroundings (the water)
4. raising the temp of the water
5. which then raises the temp of bomb calorimeter
then evaluate what you are given
after this is done the question should seem pretty easy
change in enthalpy is given divide that by moles of acetylene you the get the heat transfer to water
use some calorimetery formulas q=mct find t for the water, then do the same for the transfer of heat to the bomb calorimeter and you should be able to get the answer
thats as much as i am gonna say since this forum uses the socratic method for answering problems(but i gave you a lot more then i should have
)
oh and this formula that you got of wikipedia relates total internal energy to internal energy of sys. and surr. you don't really need this to solve this problem plus its using partial derivatives and stuff nothing you need to know for this prob.