Thermodynamics. Find the Mass Flow Rate of the Air and the Exit Area

[Northbysouth]

Homework Statement

Air expands through a turbine from 8 bar, 960 K to 1 bar, 450 K. The inlet velocity is small compared to the exit velocity of 90 m/s, The turbine operates at a steady state and develops a power output of 2500 kW. Heat transfer between the turbine and it's surroundings and potential energy effects are negligible. Modeling air as an ideal gas, calculate the mass flow rate of air, in kg/s, and the exit area, in m²

Homework Equations

m' = ρvA

ρ = p/RT

du = dQ - dw

h = u + pv

₁Q₂+m'_i(h_i+v²_i/2 + gz_i) = m'_e(h_e + v_e²/2 + gz_e)

p₁ = 800,000 Pa
T₁ = 960 K
v₁ = 0m/s

p₂ = 100,000 Pa
T = 450 K
v₂ = 90 m/s

The Attempt at a Solution

Using du = dQ - dw I know that

dw = -2500 kW

I also have:

m'_i(h_i) = m'_e(h_e + v²_e/2)

To calculate enthalpy

h = pv

h_i = 2500 kW
h_e = 2500 kW + (100,000 Pa)(90 m/s)
h_e = 11500000 W

With this information I should then be able to plug it into the large equation (The 1st law of thermodynamics I believe) and hence get m_i

But when I do this I get m_i = 0.2777 kg/s which isn't right. My TA said the answer is round about 4 kg/s.

Help is appreciated. Thank you

 

[LawrenceC]

Enthalpy is Cp*T.