This tool offers three common approaches (choose in the “Method” dropdown). All methods start from \((P_r,T_r)\).
1) Generalized chart (smooth approximation)
A stable, educational approximation that behaves like a generalized chart lookup. It’s useful for intuition and quick plotting.
2) Lee–Kesler virial (explicit; best for small \(P_r\))
A compact explicit correlation written in terms of reduced temperature and an acentric-factor correction:
\[
B_0 = 0.083 - \frac{0.422}{T_r^{1.6}},\qquad
B_1 = 0.139 - \frac{0.172}{T_r^{4.2}},
\]
\[
Z = 1 + (B_0 + \omega\,B_1)\,\frac{P_r}{T_r}.
\]
This explicit form is typically most reasonable for small to moderate reduced pressures; at larger \(P_r\), an EOS or table-based method is preferred.
3) Peng–Robinson EOS (cubic; robust)
A cubic equation of state often used for engineering calculations. In reduced form:
\[
A=0.45724\,\alpha\,\frac{P_r}{T_r^2},\qquad
B=0.07780\,\frac{P_r}{T_r},
\]
and \(Z\) is obtained from the cubic (the calculator uses the gas-phase root).
