thermal_efficiency.py

from fractions import Fraction
def in_out_heat(a,b,c,d):
    A=4*(c-a)*(d-b)
    B=b*(c-a)*Fraction(3,2)+a*(d-b)*Fraction(5,2)
    if B*(A+B)>=0:
        dU=Fraction(3,2)*(c*d-b*a)
        dW=(b-d)*(a+c)*Fraction(1,2)
        dQ=dU-dW
        if B>=0 and A+B>=0:
            return (dQ,0)
        else:
            return (0,-dQ)
    else:
        t0=Fraction(-B,A)
        x=(c-a)*t0+a
        y=(d-b)*t0+b
        dQin1,dQout1=in_out_heat(a,b,x,y)
        dQin2,dQout2=in_out_heat(x,y,c,d)
        return (dQin1+dQin2,dQout1+dQout2)

def thermal_efficiency(cycle):
    N=len(cycle)
    Work=0
    for i in range(N):
        a=cycle[i][0]
        b=cycle[i][1]
        c=cycle[(i+1)%N][0]
        d=cycle[(i+1)%N][1]
        dW=(b-d)*(a+c)*Fraction(1,2)
        Work+=dW
    if Work>0:
        return None
    IN=0
    OUT=0
    for i in range(N):
        a=cycle[i][0]
        b=cycle[i][1]
        c=cycle[(i+1)%N][0]
        d=cycle[(i+1)%N][1]
        dQin,dQout=in_out_heat(a,b,c,d)
        IN+=dQin
        OUT+=dQout
    return 1-Fraction(OUT,IN)

cycle=[(1,1),(2,1),(2,2),(1,2)]
print(thermal_efficiency(cycle))
#2/13

cycle=[(1,1),(2,1),(1,2)]
print(thermal_efficiency(cycle))
#16/97

cycle=[(1,1),(2,2),(1,2)]
print(thermal_efficiency(cycle))
#1/12

cycle=[(1,1),(2,1),(2,2)]
print(thermal_efficiency(cycle))
#1/13