Thermodynamics problem, calculate energy transfer?

[kawf]

Homework Statement

A mass of 5 kg of steam is contained within a piston cylinder assembly. The steam undergoes an expansion from its initial state with e1 = 3000 kJ/kg to its final state with e2 = 2500 kJ/kg. During the process there is a heat transfer of 80 kJ to the steam. Also, a paddle wheel transfers 10 kJ of work to the steam. Calculate the amount of energy transfer by work from the steam on the piston during the process.

Homework Equations

dE = del Q - del W

The Attempt at a Solution

Would this be correct?
W = del Q - dE
= (80kJ + 10kJ) - (2500 kJ/kg - 3000 kJ/kg)
W = 590 kJ

I don't believe this is correct but it's all I have been able to come up with so far. Any guidance is appreciated

 

[MexChemE]

Determining ΔE
$$\Delta \hat{E} = 2500 \frac{kJ}{kg} - 3000 \frac{kJ}{kg} = -500 \frac{kJ}{kg}$$
$$\Delta E = 5 \ kg \left( - 500 \frac{kJ}{kg} \right) = -2500 \ kJ$$
Now, applying an energy balance on the cylinder (1st Law of Thermodynamics)
$$\Delta E = Q + W_s - W$$
Where W_s is the work input by the paddle wheel and W is the work output on the piston. Finally
$$W = Q + W_s - \Delta E = 80 \ kJ + 10 \ kJ - (-2500 \ kJ) = 2590 \ kJ$$