Integrating gives P = K 0 ln ⁡ ⁡ ( V 0 / V ) V = V 0 exp ⁡ ⁡ ( − − P / K 0 ) E = E 0 + K 0 ( V 0 − − V + V ln ⁡ ⁡ ( V / V 0 ) ) . A more sophisticated equation of state was derived by Francis D. Murnaghan of Johns Hopkins University in 1944. To begin with, we consider the pressure