Thermodynamics Assignment (3RD YEAR engineering Thermodynamics)

[Dreamsword]

Hi Guys/Girls I require your help or assistance with the following Thermodynamics Assignment.

 

I have a few ideas however my solutions are incomplete.

 

The assignment questions can be seen below in the image.

 

I have attempted questions 2 and 3 and would like to know if I'm correct / along the right path.

 

My solution

__________

 

2) With reference to the question about the compressor

 

I've taken 100% efficiency to mean , fully reversible.

 

assumptions : steady state and adiabatic.

I've assumed that air is an ideal gas throughout the compressor.

change in entropy = 0

change in entropy of an ideal gas = 0 ( to calc the exit temperature of the compressed air )

calculated Delta H = work done by the compressor.

 

3) With reference to the Turbine question again Ive assumed the same conditions as with the compressor.

My initial thought is to split the mixture going into the turbine and calculate the change in entropy and enthalpy for each substace.

 

1) Have no idea how to prove this.

 

 

 

 

 

Edited March 22, 2016 by Dreamsword

[studiot]

Your picture is too small to read.

 

 

When you repost it, please also say specifically what your question is, this is too general.

[Dreamsword]

Please see updated post.

[studiot]

You are looking along the right lines, but rather than develop you own version Brayton analysis you should get a solid grasp of the conventional one.

 

The Brayton cycle is also called the constant pressure cycle or the Joule cycle.

 

The first thing to notice is that the machine arrangement as diagrammed is an open system and you need a closed cycle to create an analysis.

 

The idea is to chose a working fluid (air or air/fuel as an ideal gas) and develop a cyclic process involving it.

 

We do this by choosing to consider cycling our working fluid round four stages. (so there is no air input or output)

 

Instead of combustion, heat is considered added from an external source at constant pressure (Cp times the temperature change) in the second stage of the cycle and a different quantity of heat is rejected to atmosphere in the final stage.

This approach leads to some very simple equations.

All the combined fuel and air is considered as a single ideal gas.

 

I have outlined this in the attached diagrams.

We can discuss these further if you like.

 

 

[Dreamsword]

Good day thank you for your response.

 

My follow up question would then be how do I apply this to the Turbine for which I have combustion products and not just air entering the Turbine.

[studiot]

I'm not sure you have fully appreciated my initial offering.

 

The theory of heat engines depends upon working in a cycle.

This means that we end up where we started with a mass of working fluid'.

That is the working fluid is returned to its initial state. If heat or work is added somewhere in the cycle then it must be removed somewhere else in the cycle.

 

The Brayton cycle is paticularly important to understand as it forms the basis of lots of different types of heat engine.

 

 

The work integral around the cycle of such a machine is equal to the difference between the heat received at one temperature minus the heat rejected at another.

 

[math]\oint {W = {\rm{Heatreceived}}\;{\rm{ - }}\;{\rm{Heatrejected}}} [/math]

 

Four stages are identified and it is good to work per unit mass of circulating fluid.

 

 

1 - 2 :

 

Adiabatic isentropic compression according to the law [math]P{V^\gamma } = C[/math]

Pressure increase from P₁ to P₂

Temperature increase from T₁ to T₂

Volume decreases from V₁ to V₂

Entropy remains constant S₁ = S₂

 

 

 

 

 

2 - 3

 

 

Constant pressure heat addition

This can be caluclated from the heat (enthalpy) of combustion, assuming complete combustion or by applying C_p(T₃ - T₂)

Pressure remains constant at P₂ = P₃

Temperature increases from T₂ to T₃

Volume increases from V₂ to V₃

Entropy increases from S₂ to S₃

 

3 - 4

 

_{Adiabatic isentropic expansion according to the law [math]P{V^\gamma } = C[/math]}

_{Pressure decrease from P3 to P4}

_{Temperature decrease from T3 to T4}

_{Volume increases from V3 to V4}

_{Entropy remains constant S3= S4}

 

 

4 - 1

 

 

Constant pressure heat rejectionThis can be calculated from by applying C_p(T₄ - T₁)

Pressure remains constant at P₄ = P₁

Temperature decreases from T₄ to T₁

Volume decreases from V₄ to V₁

Entropy decreases from S₄ to S₁

 

You have been given some of the pressures, temperatures etc and can use these stages to calculate the missing ones and thus answer the questions.

 

Beware that some temperatures are stated in absolute and some in centigrade in your diagram.

 

To test for condensation you then have the PVT within and through the turbine to compare against a state diagram for water.