function dP_dV = gas_constitutive_reln(V,P)

R = 8.314;
n = (0.2*10^6*3.741721938165305e-08)/(R*293);

a = 28110*10^-3;
b = 1.967*10^-3;
c = 0.004802*10^-3;
d = -1.966*10^-6*10^-3;
e = 0;

T = P*V/(n*R);
Cp = a+b*T+c*T^2+d*T^3+e/T^2;
RHS = -(P/V)*(Cp/(Cp-R));

dP_dV = RHS;