# Carnot engines

#### zandbera

1. 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.

2. Homework Equations
e = Weng / Qh = 1 - Qc / Qh
PV/T = constant ( i think)

3. The Attempt at a Solution
for part a), i used PV/T = constant to try and figure out the temperature, but Im not given a volume, and i dont know how to figure it out. im assuming you have to use the flow rate, 80.0kg/min but i dont know how. i have the equation for the final temperature:

Tf = (800 C)(1.5MPa)Vf / (300 kPa)Vi

but i dont know the volumes, and i also dont understand why the pressure drops. i know that as the velocity of something moving through a hole increases the pressure decreases so is that whats 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

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#### Redbelly98

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

#### Andrew Mason

Science Advisor
Homework Helper
1. 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.

2. Homework Equations
e = Weng / Qh = 1 - Qc / Qh
PV/T = constant ( i think)

3. The Attempt at a Solution
for part a), i used PV/T = constant to try and figure out the temperature, but Im not given a volume, and i dont know how to figure it out. im assuming you have to use the flow rate, 80.0kg/min but i dont know how. i have the equation for the final temperature:

Tf = (800 C)(1.5MPa)Vf / (300 kPa)Vi

but i dont know the volumes, and i also dont understand why the pressure drops. i know that as the velocity of something moving through a hole increases the pressure decreases so is that whats 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 dont know the final and initial volumes so how does that help?

#### Redbelly98

Staff Emeritus
Science Advisor
Homework Helper
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

Staff Emeritus
Science Advisor
Homework Helper
No. Use this equation to find the ratio Vf/Vi:
zandbera said:
PiVi^y = PfVf^y where y = cp/cv

#### zandbera

Ohhhhh okay I think I get it now. Thanks

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