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Homework Statement:
 Air with a volume of 1.59 m^3 at 2.06267 atm and 298.7 K is compressed by a compressor, which applies 260 kJ/kg of flow work to increase the pressure to 2,094 kPa. Find the final temperature in Kelvin.
Relevant Equations:

First Law of Thermodynamics
Energy Balance Equation for Open Systems
Ideal Gas Equation
h = Pv + u
Hi
I'd like to know if my current approach to the problem has any issues.
My attempt:
Balancing the equation:
Q_{in} + W_{in} +mΘ_{out} = Q_{out} + W_{out} + mΘ_{out}
Q_{in}+m(h_{in} + v^{2}_{in}/2 + gz_{in}) = m(h_{out} + v^{2}_{out}/2 + gz_{out})
W_{flow} + ΔU + m(h_{in}) = m(h_{out})
I factored out the mass:
w_{flow} + Δu + h_{in} = h_{out}
And I used h = Pv +u where h = specific enthalpy, P=pressure, v=specific volume, u=specific internal energy, to get:
w_{flow} = P_{2}v_{2}  P_{1}v_{1}
I then used the ideal gas equation Pv = RT, with R = 0.287 kJ/kg*K and P = 2.06267 atm = 209 kPa to get v_{1}
v_{1} = (0.287 kJ/kg*K)(298.7 K) / (209 kPa) = 0.4102 m^{3}/kg
And plugged it in the previous equation for v_{2}
v_{2} = (w_{flow} + P_{1}v_{1}) / P_{2}
v_{2} = [260 kJ/kg + (209 kPa)(0.4102)]/(2,094 kPa) = 0.1651 m^{3}/kg
I then used the ideal gas equation again to solve for T_{2}.
Any insight would be greatly appreciated.
I'd like to know if my current approach to the problem has any issues.
My attempt:
Balancing the equation:
Q_{in} + W_{in} +mΘ_{out} = Q_{out} + W_{out} + mΘ_{out}
Q_{in}+m(h_{in} + v^{2}_{in}/2 + gz_{in}) = m(h_{out} + v^{2}_{out}/2 + gz_{out})
W_{flow} + ΔU + m(h_{in}) = m(h_{out})
I factored out the mass:
w_{flow} + Δu + h_{in} = h_{out}
And I used h = Pv +u where h = specific enthalpy, P=pressure, v=specific volume, u=specific internal energy, to get:
w_{flow} = P_{2}v_{2}  P_{1}v_{1}
I then used the ideal gas equation Pv = RT, with R = 0.287 kJ/kg*K and P = 2.06267 atm = 209 kPa to get v_{1}
v_{1} = (0.287 kJ/kg*K)(298.7 K) / (209 kPa) = 0.4102 m^{3}/kg
And plugged it in the previous equation for v_{2}
v_{2} = (w_{flow} + P_{1}v_{1}) / P_{2}
v_{2} = [260 kJ/kg + (209 kPa)(0.4102)]/(2,094 kPa) = 0.1651 m^{3}/kg
I then used the ideal gas equation again to solve for T_{2}.
Any insight would be greatly appreciated.