A theoretical study of the thermodynamics of gas expansion from a high-pressure to a low-pressure tank

In engineering practice and thermodynamics texts, it is assumed that, for the expansion of a gas from a high-pressure tank to a low-pressure tank (through a valve) under adiabatic conditions, the process in the high-pressure tank is isentropic. No theoretical explanation or experimental proof is, however, cited in support of this assumption. A thorough theoretical investigation of this question is presented in this paper. The present numerical computation with an unsteady simulation using the first law of thermodynamics and with no explicit assumption regarding the thermodynamic process that takes place in the high-pressure tank establishes that the expansion in the high-pressure tank is indeed isentropic. Although an analytical proof has not been formulated, it is believed that the present computations constitute the first theoretical justification for the much-used isentropic assumption found in thermodynamics textbooks. A direct determination of a steady solution using an average exit enthalpy for the high-pressure tank also gives a correct result if the pressure ratio in the high-pressure tank is limited to 2. Even though the gas expansion in the high-pressure tank turns out to be isentropic, it is shown that the overall process of gas expansion and compression to the low-pressure tank is an irreversible process. © Manchester University Press.