two moles of a monoatomic gas are contained at pressure 1 atm and teperature 300

Question

two moles of a monoatomic gas are contained at pressure 1 atm and teperature 300 k. 34,  166 joules of heat are transfered to the gas as a result the gas expands and does work on the surroundings of 1214 joules. The process is reversible, calculate the final temperature.

I'm stuck on this for the last two hours I've tried finding the internals energy change, and specific heat with constant volune but I can't seem to find how work is going to relate to an equation to find temperature 2 or the change in enegy.

Explanation / Answer

Q = nR(delta T) + n*Cv*(delta T)

166 - 1214 = 2*8.314*(1+1.5)*(delta T)

delta T = -1048/(2*8.314*2.5)

= -25.2 K K

Final T = 300 - 25.2

= 274.75 K

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