plot p-V-diagramm cycle process

hey guys,

For my study I need to plot a p-V-diagramm,

here are the data:

adiabaric compression:

T1 = 343.15 K, T2 = 423.15 K

p1 = 100000 Pa, p2 = 152061.995 Pa

V1 = 0,0285 m^3, V2 = 0.0243 m^3

isobar compression:

T3 = 423.15 K, T4 = 343.15 K

p3 = 152061.995

V3 = 0.0243 m^3, V4 = 0.0197 m^3

isothermal expansion:

T5 = 343.15 K

p5 = 152061.995 Pa

p6 = 100000 Pa

V5 = 0.0197 m^3

V6 = 0.0285 m^3

I tried to plot it with folowing code:

% adiabaric compression
Vv2 = linspace(0.0285, 0.0243, 42);
Vv1 = 0.0243;
% [T1m,V1m] = ndgrid(Tv1,Vv1);
R = 8.314472;
n = 1;
p1=100000;
p=zeros(42,1);
kappa =  20.78618/12.471708;
i=1;
while i<=42
    p(i) = (p1*(Vv1^kappa))./(Vv2(i)^kappa);
        i=i+1;
end


% isobar compression
p3=linspace(152061, 152061, 42);
Vv3 = linspace(0.0243, 0.0197, 42);

% isothermal expansion
T = 343.15;
m=1;
Vv4 = linspace(0.0197, 0.0285, 88);
% p4 = (m*R*T)./Vv4;
% p4 = @(T,V) m*R*T./V;
p4=1.520619949963026e+05;
p5=zeros(88,1);
Vv34 = 0.0197;
j=1;
while j<=30
    p5(j) = (p4*Vv34)./(Vv4(j));
        j=j+1;
end

figure
plot (Vv2, p);
hold on
plot(Vv3, p3);
hold on
% plot(Vv4, p5(T,Vv4));
plot(Vv4, p5);
hold off
title('p-V-diagram')
xlabel('volume V [m^3]')
ylabel('Pressure p [Pa]')
% axis([0.02  0.03    0.5*10^5  2.1*10^5])
legend('adiabaric compression', 'isobar compression', 'isothermal expansion')

The diagramm should look like in picture in the attachment. Can someone help me to plot this diagram or explain how I can solve it numericly?

Best regards

Answer 1

[Poorna]

Hi Alex,

I understand that you want to plot the PV graph for the given compressions and expansions so that the resulting graph looks similar to the reference graph.

Initially, it is important to note that there are some imperfections in the given constants.

• For an isothermal process PV should be constant, but p5*v5 is not equal to p6*v6.
• For an adiabatic process PVɣ should be constant. The adiabatic constant that you calculated in line 9 evaluates to 5/3. But again p1*(v1^(5/3)) is not equal to p2*(v2^(5/3)).

So, I suggest you recheck the values so that all the conditions are satisfied.

Once you get all the values correct you can generate the data points for all the plots as below:

• Adiabatic compression

v_adiabatic = linspace(0.0243, 0.0285, 42); 
p_adiabatic = p1*(v1^kappa) ./ (v_adiabatic .^ kappa);

• Isobaric compression:

v_isobar = linspace(0.0243, 0.0197, 42); 
p_isobar = linspace(152061, 152061, 42); 

• Isothermal expansion

v_isothermal = linspace(0.0197, 0.0285, 88); 
p_isothermal = p5*v5 ./ v_isothermal; 

Hope this Helps!