Solving Argon's Turbine Expansion Problem

[zandbera]

Homework Statement

Argon enters a turbine at a rate of 80.0 kg/min, a temperature of 800^.C, and a pressure of 1.50 MPa. It expands adiabatically as it pushes on the turbine blades and exits at pressure 300 kPa. (a) Calculate its temperature at exit. (b) Calculate the maximum power output of the turning turbine. (c) The turbine is one component of a model closed-cycle gas turbine engine. Calculate the maximum efficiency of the engine.

Homework Equations

e = W_eng / Q_h = 1 - Q_c / Q_h
PV/T = constant ( i think)

The Attempt at a Solution

for part a), i used PV/T = constant to try and figure out the temperature, but I am not given a volume, and i don't know how to figure it out. I am assuming you have to use the flow rate, 80.0kg/min but i don't know how. i have the equation for the final temperature:

T_f = (800 C)(1.5MPa)V_f / (300 kPa)V_i

but i don't know the volumes, and i also don't understand why the pressure drops. i know that as the velocity of something moving through a hole increases the pressure decreases so is that what's happening? and i also know that as the volume drops, the pressure increases( i think?), so that would mean that Vf would be higher?

i just need some guidance on this one

 

[Redbelly98]

The key here is adiabatic expansion. What is the relation between P and V in that case (doesn't involve temperature)?

 

[Andrew Mason]

Homework Statement

Argon enters a turbine at a rate of 80.0 kg/min, a temperature of 800^.C, and a pressure of 1.50 MPa. It expands adiabatically as it pushes on the turbine blades and exits at pressure 300 kPa. (a) Calculate its temperature at exit. (b) Calculate the maximum power output of the turning turbine. (c) The turbine is one component of a model closed-cycle gas turbine engine. Calculate the maximum efficiency of the engine.

Homework Equations

e = W_eng / Q_h = 1 - Q_c / Q_h
PV/T = constant ( i think)

The Attempt at a Solution

for part a), i used PV/T = constant to try and figure out the temperature, but I am not given a volume, and i don't know how to figure it out. I am assuming you have to use the flow rate, 80.0kg/min but i don't know how. i have the equation for the final temperature:

T_f = (800 C)(1.5MPa)V_f / (300 kPa)V_i

but i don't know the volumes, and i also don't understand why the pressure drops. i know that as the velocity of something moving through a hole increases the pressure decreases so is that what's happening? and i also know that as the volume drops, the pressure increases( i think?), so that would mean that Vf would be higher?

i just need some guidance on this one

There is a particular relationship between P and V during an adiabatic expansion. It has to do with the fact that as the gas expands and does work, the energy to do that work must come from the internal energy of the gas. The adiabatic condition must be used to determine the termperature of the gas during an adiabatic expansion.

AM

 

[zandbera]

well for an adiabatic expansion i know that PiVi^y = PfVf^y where y = cp/cv, but i don't know the final and initial volumes so how does that help?

 

[Redbelly98]

You don't need the actual volumes, you just need their ratio Vf/Vi.

 

[zandbera]

Which is equal to the ratio of the final and initial pressures?

 

[Redbelly98]

No. Use this equation to find the ratio Vf/Vi:

PiVi^y = PfVf^y where y = cp/cv

 

[zandbera]

Ohhhhh okay I think I get it now. Thanks