# Thermodynamics - Control Volumes find final temperature

• Engineering

## 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:
Qin + Win +mΘout = Qout + Wout + mΘout
Qin+m(hin + v2in/2 + gzin) = m(hout + v2out/2 + gzout)
Wflow + ΔU + m(hin) = m(hout)

I factored out the mass:
wflow + Δu + hin = hout
And I used h = Pv +u where h = specific enthalpy, P=pressure, v=specific volume, u=specific internal energy, to get:
wflow = 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 = (wflow + 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.