# Plotting isothermals and adiabats

first time poster in this site.

I am trying to create a small program to make a graph of the Carnot cycle.

For isothermals I am simply trying to look for points where P*V would give the same Temperature so that I can display an isothermal curve.

However, I am having absolutely no luck with trying to plot an adiabatic curve. I know I want a steeper curve, but thats about it. Is there some sort of simpler way to draw out an adiabatic curve? Can I set any variable constant and try to draw the curve like an isotherm?

Any information is appreciated.

        //ISOTHERMS
//i = x axis; j = y axis;
// for values 1 - 350
// plot y values from isothermal equation -- P*V = constant T
// j = k/i

int k1 = 5000;
//int k1 = 1500;
//int k1 = 15000;
//int k2 = 20000;
int k2 = 15000;
//int k2 = 30000;

g.setColor(Color.red);
for( int i = 1; i < 350; i++)
{
int j1 = k1/i;
int j2 = k2/i;
//if(j1 < 350)
g.drawLine(i+50, j1+50, i+50, j1+50);
//if(j2 < 350)
g.drawLine(i+50, j2+50, i+50, j2+50);

}

//ADIABATS
//P*V^gamma = constant T
double gamma = 1.67;

for( int m = 1; m < 500; m++)
{

// int h1 = (int) (1400000/(Math.pow(m,1.97)));
int h1 = (int) (1000000/(Math.pow(m,2)));
//int h2 = (int) (3500000/(Math.pow(m,1.97)));
int h2 = (int) (2400000/(Math.pow(m,2)));
//if(j1 < 350)
g.setColor(Color.blue);
g.drawLine(m+50, h1+50, m+50, h1+50);
//if(j2 < 350)
g.drawLine(m+50, h2+50, m+50, h2+50);

}


## 1 Answer

$PV^{\gamma}=Const$, where $\gamma = C_p/C_v$

• Bear with me, but am I applying the exponent to (P*V) or only one of the two? so if i choose a monatomic and gamma is 1.67, do I write (x *y)^1.67 = Const? Also, since I have to tell the program to draw the points when the equation equals the constant in question, i'm having difficulty finding even a constant to attempt drawing. – lralvare Feb 26 '16 at 19:03
• To get the constant, substitute the P and V at the end of the isothermal step. – Chet Miller Feb 26 '16 at 19:16
• If I wanted to write P in terms of V; would I write it as something like... P = (Const/V)^(- gamma ) ? I have to write it this way in the program to make the plot points cleaner. – lralvare Feb 29 '16 at 9:31
• made an attempt, though I'm sure I didn't do the correct equation with game since the adiabatic slopes taper off too quickly i think with greater X (volume). – lralvare Feb 29 '16 at 10:10
• I have no idea what you are saying. $P=P_1(V_1/V)^{\gamma}$ – Chet Miller Feb 29 '16 at 12:18