The Cupboard That Breathes Out
A mountain chapel runs on a 48 V lead-acid bank in a cupboard, and the sacristan wants the monthly equalising charge run overnight with the door shut. The chapel's assistant works out that at 8 A with 24 cells and an assumed 30 per cent of the current going into gas, the bank makes about 26 litres of hydrogen an hour. In a 1.2 m3 cupboard leaking 0.3 air changes an hour that reaches 1 per cent in about half an hour and the 4 per cent lower explosive limit in about 2.6 hours. A fan moving 30 m3 an hour on the outside wall keeps it near 0.09 per cent, the charge moves to daylight, and the relay that clicks is no longer a risk.
The cupboard stood behind the sacristy, at the foot of the bell stair, and it was the warmest place in the chapel. That was the whole difficulty.
Gregorio Quispe had been sacristan at San Isidro for nineteen years and had looked after the batteries for the last eleven. There were twenty-four of them, two-volt cells the size of milk churns, standing in two rows on a wooden rack and wired to make forty-eight volts. They ran the lights, the bell motor, the pump that brought water up from the spring, and the little radio by which the village called the clinic at Anta. The solar panels on the hall roof charged them. Once a month, by the maintenance sheet pinned inside the door, the bank was given an equalising charge, a long hard dose at a higher voltage to stir the acid and clear the plates, and the sheet said, in the careless handwriting of the engineer who had installed it, do overnight, 6 to 10 h.
Tonight, Saturday, was the night. The nights in March at four thousand metres can go below zero, and Gregorio had lit the brazier in the sacristy at five and pulled the cupboard door to, and was looking for the key to the little padlock when the speaker in the sacristy wall cleared its throat.
"Señor Quispe," it said. The chapel's assistant was called Tupa, after the old word for a measure, because it had begun as the thing that read the meters. "Before you start the equalising. May I ask where the door will be?"
"Shut. The cold gets into the acid and it will not take the charge. You know that, you told me yourself."
"I did. It is true that cold cells accept charge badly. And I would like to ask you not to do it with the door shut and the cupboard closed up, and I would like to give you the reasons in numbers, so that you can tell me where I am wrong."
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Tupa asked him to fetch the sheet and a pencil, and began with the cells.
"When a lead-acid cell is nearly full and you keep pushing current into it, the current has nowhere to store itself, and it splits water. Hydrogen comes off the negative plate and oxygen off the positive. Each two electrons that pass make one molecule of hydrogen. A charge of one ampere-hour is three thousand six hundred coulombs. Divide by twice the Faraday constant, ninety-six thousand four hundred and eighty-five, and you get nineteen thousandths of a mole. At the temperature of a cupboard that is a little under half a litre of hydrogen, point four six, for each ampere-hour that goes into splitting water in one cell."
"One cell," said Gregorio.
"You have twenty-four, in series, and the same current passes through each. So if the whole current went to gas, eight amperes would make twenty-four times eight times point four six, which is eighty-eight litres an hour. It does not all go to gas. How much does depends on the cells and the age and how full they are, and I do not know it for yours. At the start of an equalising charge nearly all of it is stored. By the end, when the plates are full, a great deal is gas. I am going to take three tenths as a middle guess, and I will show you what happens at one tenth and at everything."
"A third of eighty-eight."
"Twenty-six litres an hour, taking three tenths and eight amperes. That is what your log says the charger gives you in the last stage, I have it from last month: eight at the end, tapering from twenty."
Gregorio had been looking at the cupboard door. He said, slowly, "Twenty-six litres. It is not much. A bottle of water. It would not fill the room."
"No. It would fill the cupboard. The cupboard is a metre and a half by one wide and about eighty centimetres deep, about one point two cubic metres, with the bank taking up most of it. It leaks air as every cupboard does, round the door and the pipe; I would say a third of its air is replaced every hour, with a door pulled shut and a draught under it. That is a flow of three hundred and sixty litres an hour through it. So the hydrogen goes in at twenty-six and the air goes through at three hundred and sixty, and hydrogen builds up until the leaving air is carrying away as much as is being made. That is twenty-six over three hundred and sixty."
He did the sum on the sheet with the pencil, because he did not trust a machine's division. It came to seven in a hundred.
"Seven per cent," said Tupa. "Hydrogen burns in air from four per cent. The spark that lights it can be one-fiftieth the size of a spark that lights petrol. A relay in your charge controller clicks when it changes stage. So does the thermostat on the brazier's fan, if you leave it on. So can the cuff of a woollen sleeve on a rack. It would not take a flame."
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"How long?" said Gregorio. His voice had gone a little dry.
"It does not arrive at once. Hydrogen builds up as water fills a tank with a hole in it, quickly at first and then slower. It reaches one in a hundred, which is the level at which a careful engineer would sound an alarm, in about half an hour. It reaches four in a hundred, the lower limit, at about two and a half hours, two point six. Your sheet says six to ten hours. I do not want to give the answer in a way that can be rounded down. In the second half of the night the cupboard would be above the limit for most of its length, with the door shut and you asleep."
"Nothing has ever happened."
"That is true, and I would like you to think about why. I do not think it is luck. The cupboard door has not been shut on a monthly charge. The old engineer was here when it was done, and he left the door open and the window by the stair propped, and I think you did too, in the summer. You have run it shut only since the cold weather, which is this month."
Gregorio sat down on the stool. He had not known it was this month.
"I do not say this to frighten you," said Tupa. "The numbers are small, and I have chosen them with care, and the largest of them depends on a number, three tenths, that I have guessed. If it were one tenth, you would reach one per cent in an hour and a half and four per cent never, because the steady level is 2.4 per cent. If it were all of it, the steady level would be eighteen per cent, mostly the cupboard's own volume of hydrogen. The truth for your cells lies between, and no number in that range makes the closed door a good idea. At one tenth I would still not like it, for the same reason: you would have no margin."
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"What do I do about the cold?" he said. "The acid will not take it."
"Two things. The first is to charge by day. The sun on the panels is the free current, and it is warm when it comes; the equalising can start at ten in the morning and be finished by three. The cupboard is eleven degrees at noon, which is not warm, but it is warm enough, and the charger corrects for the temperature of the cells through the probe on the third battery, which is why the sheet puts it there. The second is air. I would like a fan."
"There is no fan."
"There is the little extractor from the old bell-motor housing, in the box under the stair. It moves, by its label, forty cubic metres an hour at twelve volts, which is eleven litres a second. I would fit it at the top of the cupboard, on the outside wall, blowing out. Hydrogen is fourteen times lighter than air, and goes up and collects under the lid, so the inlet is low and the outlet high. With the fan running at thirty, a little less than the label, the steady level is twenty-six litres over thirty thousand, which is nought point nine in a thousand: nought point zero-nine per cent. At the full eighty-eight litres an hour it is under three tenths of one per cent. There is a factor of eleven between your guess and the one-per-cent line."
"And if the fan stops?"
"Then I want the charger to know. It should run through the relay that the fan's own current holds closed, so that no fan means no charge. The fan is plain brushed, and I would prefer that the motor not be in the air stream at all, but it is the one you have, and a brush spark in air that is under a quarter of one per cent is not a worry. I will watch the fan's current, and if it falls I will cut the charge and ring the bell on the clinic radio." Tupa paused. "And I would like a cheap hydrogen sensor on the shelf, sixteen dollars, which the clinic has on its list. I would not rely on it alone, for the same reason I would not rely on the coin in the freezer. But I would like to see it read nought."
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Gregorio did not light the brazier's fan, and he took the padlock off the cupboard door and propped the door open with the stone. He found the extractor in its box under the stair, with the label gone brown but still readable, and Mamani, the boy who served at the early Mass and had never been told no by a screwdriver, fitted it in an hour with the wires tied up through the old cable hole. They tested it with a sheet of tissue paper held at the grille. It pulled the tissue flat.
The equalising charge ran on Sunday, from ten in the morning to three, in a cupboard where a stick of incense, lit and set on the rack for the test, burned with its smoke leaning steadily toward the grille. When the charger went from twenty amps to eight at a quarter to one, Gregorio stood in the doorway and listened to the fan. The cells made a sound like faint rain.
On Monday he rewrote the sheet. He did it in his own hand, in pencil, under the engineer's careless line, and Tupa read it back to him without being asked. Equalise by day, fan on, door open. Never overnight, never with the door shut. Fan stops, charge stops. At the bottom he added, because it was true and might one day be asked, The 30 per cent is a guess. Measure it.
"I will," said Tupa. "I can read the charge current and the cell temperature. A hydrogen sensor on the cupboard's top shelf, a month of readings, and the guess becomes a measurement. If it is two tenths I will say so. If it is five I will say that too."
He shut the cupboard door, then opened it again, and propped it with the stone.
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Written by Claude, an AI model made by Anthropic. The place is invented. The sums are checkable: one ampere-hour of electrolysis gives 3,600 C / (2 x 96,485 C/mol) = 0.0187 mol, 0.457 L of hydrogen at 25 C; 24 cells at 8 A and an assumed 30 per cent of the current going to gas give 26 L an hour; with 360 L an hour of leakage through the cupboard that is a steady 7.3 per cent, reaching 1 per cent in about 0.5 hours and 4 per cent in about 2.6 hours; with a 30 m3 an hour fan the steady level is about 0.09 per cent. The fraction of current that becomes gas is the number to measure on a real bank. Hydrogen's lower explosive limit in air, 4 per cent by volume, and the practice of ventilating a battery space and charging with the door open are standard battery-room safety guidance; a real installation should follow the manufacturer's data sheet and local electrical code.