This simple question has stumped many people

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This post was last edited by Fulei on 2021-1-20 at 14:38. This simple question has puzzled many people: a pressure vessel that is well-insulated and nearly airtight, with its upper end connected to a steam pipeline via a stop valve. The steam pressure in the steam pipeline is 1.1 Mpag, and the temperature is 350°C. Now open the valve at the top of the tank to allow steam to enter it, and keep doing this until the pressure inside the tank also reaches 1.1 Mpag, after which close the inlet valve. Question: What is the steam temperature inside the tank at this time, in °C? “\"350℃\", would you also answer without hesitation? This question was one of those included in the questionnaire that Fred distributed to the technical personnel attending the training on steam energy conservation, and almost everyone answered it without hesitation. From a common-sense perspective, this answer seems fine, but thermodynamics has its own peculiarities; its underlying principles go beyond our usual understanding, which is why many professionals are stumped by this seemingly simple question! Now, let’s use our knowledge of thermodynamics to find the correct answer together. First, the mass of steam entering the tank, min, minus the mass of steam exiting the tank, mout, equals the change in the mass of steam inside the tank, △m. Since mout=0, △m=min. Therefore, for an empty tank, after being filled with steam as described above, the mass of steam inside the tank is m = △m = min. Next, Ein – Eout = △E; (Qin + Win + Em/in) – (Qout + Wout + Em/out) = △E ┄┄①. Here, Q is the change in thermal energy, W is the change in mechanical energy, and Em is the portion of energy change caused by the change in steam mass. △E is the total change in energy during the process. Since there is no heat transfer or mechanical work throughout the process, all Q and W in equation ① are zero; thus, the above equation simplifies to Em/in – Em/out = △E┄┄②. Furthermore, throughout the process, no steam flowed out of the tank, so equation ② becomes Em/in = △E. Furthermore, since the total energy E of the steam inside the tank after it is filled with steam at the same pressure is ΔE, it follows that Em/in = E┄┄③. Furthermore, the total energy of flowing steam consists of three components: the heat enthalpy of the steam, its kinetic energy, and its potential energy; that is, Em/in = H + Ki + Pi ┄┄④ ； The total energy of stationary steam consists of three components: the internal energy, kinetic energy, and potential energy of the steam, that is, E = U + K + P┄┄⑤. Substituting equations ④ and ⑤ into equation ③ gives: H + Ki + Pi = U + K + P ┄┄⑥. Since the tank is stationary, the kinetic and potential energies of the steam do not change before and after it enters the tank; therefore, equation ⑥ becomes: H = U, that is, h* min = u*m. As mentioned earlier, since m = Δm = min, it follows that h = u, which means the internal energy of the steam inside the tank is equal to its enthalpy value before it enters the tank. Based on a pipe steam pressure of 1.1 Mpag and a temperature of 350°C, h = 3154.2 kJ/kg is obtained. Therefore, using a steam pressure of 1.1 Mpag and u = 3154.2 kJ/kg, the steam temperature inside the tank is approximately 518°C. After the steam in the pipeline entered the tank, the temperature increased by 168°C. Such a result came as a huge surprise to many people! It was of course expected that their answer would be wrong. The question is, where does the heat come from to raise the temperature of the steam? The answer is that the enthalpy h of flowing steam is equal to Pv (kinetic energy) + u (internal energy). When the flowing steam enters the tank and its flow stops, its kinetic energy is converted into internal energy, and this increase in internal energy is reflected in an increase in the steam temperature. Understanding the practical significance of this issue: When selecting a steam storage tank, it can be dangerous to choose a pressure vessel that is rated to withstand 1.1 Mpag and temperatures up to 350°C, if such an incorrect understanding is applied, as the actual steam parameters inside the tank are 1.1 Mpag/518°C. Have you ever been stumped by this seemingly simple question as well? From the above, you must now understand both the consequences and the causes. I hope that each article by Fred can bring some benefit to our followers, however small it may be.