Thermodynamics - Control Volumes find final temperature

[WateryFungi]

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 + v²_in/2 + gz_in) = m(h_out + v²_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 = P₂v₂ - P₁v₁

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 v₁
v₁ = (0.287 kJ/kg*K)(298.7 K) / (209 kPa) = 0.4102 m³/kg
And plugged it in the previous equation for v₂
v₂ = (w_flow + P₁v₁) / P₂
v₂ = [260 kJ/kg + (209 kPa)(0.4102)]/(2,094 kPa) = 0.1651 m³/kg
I then used the ideal gas equation again to solve for T₂.

Any insight would be greatly appreciated.

 

[Valkarie]

Your approach looks correct. The only thing I would suggest is to double check all of your calculations to make sure you haven't made a mistake. Additionally, it might be helpful to include a step-by-step explanation of how you arrived at the final equation to help others understand the problem.