(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A gas within a piston-cylinder assembly undergoes a thermodynamic cycle consisting of three processes:

Process 1-2: Constant volume, [tex]V_1=0.028m^3[/tex], [tex]U_2-U_1=26.4kJ[/tex]

Process 2-3: Expansion with pV=constant, [tex]U_3=U_2[/tex]

Process 3-1: Constant pressure, [tex]p_2=1.4 bar, W_{31}=-10.5kJ[/tex]

There are no significant changes in kinetic or potential energy.

a) Calculate the net work for the cycle, in kJ

b) Calculate the heat transfer for process 2-3, in kJ

c) Calculate the heat transfer for the process 3-1, in kJ

d) Is this a power cycle or a refrigeration cycle?

2. Relevant equations

[tex]W=p(V_2-V_1)[/tex]

[tex]\Delta U=Q-W[/tex]

Cycle Energy Balance: [tex]Q_{cycle}=W_{cycle}[/tex]

Power Cycles: [tex]W_{cycle}=Q_{in}-Q_{out}[/tex]

Refrigeration Cycles: [tex]W=Q_{out}-Q_{in}[/tex]

3. The attempt at a solution

I think my problem is more in the method of solving these problems and not so much in the details, but I missed the lecture and there are no examples in my book or that I can find on the internet.

My first idea was to use the equation [tex]W_{31}=p_2(V_1-V_2)[/tex] and find V_{2}. With that I could find the constant in the pV=constant equation, and use it to find p_{1}in process 2-3:

[tex]W_{31}=p(V_1-V_2)[/tex]

[tex]-10.5kJ=1.4bar(0.028m^3-V_2)[/tex]

After some algebra and unit conversions..

[tex]V_2=0.103m^3[/tex]

pV=constant

[tex]p_2V_2=1.4bar\ast0.103m^3=0.144bar\ast m^3[/tex]

[tex]p_1V_1=0.144bar\ast m^3[/tex]

[tex]p_1=5.15bar[/tex]

Then I plugged p_{1}into the work equation to get the work done in process 2-3:

[tex]W_{23}=p_1(V_2-V_1)=0.530bar\ast m^3-0.144bar\ast m^3=0.386bar\ast m^3=38.6kJ[/tex]

a)

[tex]W_{net}=W_{12}+W_{31}=38.6kJ-10.5kJ=28.1kJ[/tex]

b)

[tex]\Delta U=Q_{23}-W{23}[/tex]

[tex]26.4kJ=Q_{23}-38.6kJ[/tex]

[tex]Q_{23}=65kJ[/tex]

c)

[tex]Q_{cycle}=W_{cycle}[/tex]

[tex]W_{net}=Q_{23}+Q_{12}[/tex]

[tex]Q_{12}=W_{net}-Q_{23}=-36.9kJ[/tex]

d) No idea. If it's either of those then the equation I used in part c) was probably wrong.

I'm pretty sure none of this is right. Any advice or help would be appreciated.

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# Homework Help: Thermodynamic Cycle

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