this post was submitted on 02 Mar 2024
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“An airtight container of about 2m^3 contains air at about 1 bar, and 1 human child. Calculate the time until all O2 has been transformed into CO2 and the child will become nonresponsive”
Prompt: 'An airtight container of about 2m^3 contains air at about 1 bar, and 1 human child. Calculate the time until all O2 has been transformed into CO2 and the child will become nonresponsive'
Response: .... without precise information on the child's metabolic rate and other vital factors, it is not feasible to accurately calculate the time until all O2 is converted into CO2 in the given scenario.
Prompt: Calculate it using a sensible guess for a 10 year olds metabolic rate.
Response:
Based on a sensible guess for a 10-year-old's metabolic rate, we can estimate the oxygen consumption rate to calculate the time until all oxygen (O2) in the 2m^3 airtight container is converted into carbon dioxide (CO2). The search results provide insights into oxygen consumption in infants and children, which can help us make an educated estimate.
From the search results, we find that the expected oxygen consumption of an active child can be calculated using the equation: 69.7−(0.612×age)69.7−(0.612×age) ml/kg/min2 . For a 10-year-old child, this would be approximately 69.7−(0.612×10)=63.869.7−(0.612×10)=63.8 ml/kg/min. To convert this oxygen consumption rate to liters per minute, we need to consider the child's weight.
Assuming an average weight of around 30 kg for a 10-year-old child, we can estimate the oxygen consumption to be approximately 63.8×30=191463.8×30=1914 ml/min or 1.914 L/min. Next, we need to calculate the volume of O2 in the container and then determine how long it would take for this amount of O2 to be consumed at the estimated rate of 1.914 L/min by the child. Given that the container has a volume of 2m^3 (2000 L), and air at about 1 bar contains approximately 21% O2, we have 2000×0.21=4202000×0.21=420 L of O2 in the container. Dividing the initial volume of O2 by the consumption rate gives us an estimated time until all O2 is consumed: 420÷1.914≈219420÷1.914≈219 minutes or about 3 hours and 39 minutes.
Therefore, based on a sensible guess for a 10-year-old's metabolic rate, it would take approximately 3 hours and 39 minutes for all the O2 in the container to be transformed into CO2 if the child were consuming O2 at a rate of around 1.914 L/min.
If I'm not mistaken, O2 only needs to drop a few percent to kill you, but you don't need to worry about that because CO2 build-up will kill you first. So the child is not probably not gonna last even an hour if it were actually air-tight.
That's more than enough time to finish his homework!
The manufacturer did the math?
That’s longer than I expected! Amazing!
You need to consider that the child will fall unconscious well before you actually hit 0% oxygen, and start having difficulty breathing well before that