As part of a special day celebration (perhaps my birthday, perhaps Slashdot's 10th anniversary, or perhaps Guy Fawkes Day... it doesn't really matter), the thought occurred to me that it would be entertaining to have a "birthday cake" underwater. Obviously, once the thought had occurred to me, the science behind it became quite entertaining, and so, I pondered. What requirements must be met for it to count as a "real" birthday cake? The list was surprisingly short:
The first corollary to the third requirement, then, was obvious. The candles would require a gaseous atmosphere capable of sustaining combustion -- in short, air. Various issues immediately follow from that. First, some container must be procured to hold the air. The larger the volume of the container, the more weight will be required to offset its buoyancy. In order to reduce the problem to manageable scale, the container needs to be of relatively small volume -- an 8-pound block of lead (the largest single block I have handy) will offset a gallon of air, so that's about the size of it.
Of course, by limiting the volume of the container, we encounter other issues. Perhaps most significant of these is the oxygen consumption of the candles (as well as the heat generation which is the direct result of said consumption). Upon further thought, we consider the case of the one-year-old child. Said child's birthday cake is adorned with but a single candle, and yet, it is in no way found lacking in birthday-cake-ness. With that in mind, reducing the number of candles to a single representative candle should not invalidate the procedure, and it significantly reduces the oxygen consumption and heat generation parameters versus multiple candles.
On a similar note, the physical size of the cake has not been shown to be of particular importance. In fact, the size of the cake is almost always a function of the size of the guest list, a parameter which has no defined correlation to the number of candles (or any parameter from which the number of candles is derived). Therefore, as long as the cake-ness requirement is satisfied and there is sufficient material to anchor the sole candle, the dimensions are unimportant. While several fractional sheet cakes are often cut from a single full-sheet cake, continuing that to the point of frosting a single piece of cake would seem disingenuous, however, using one intact cupcake does not have the same stigma. (There is also a body of evidence indicating that the cupcake approach has significant force of tradition behind it, even if less than that of the full birthday cake concept.)
So, now we've defined the scope of the project to:
What is a disposable lighter, anyway? Well, at its simplest, it is a container of flammable fluid, a valve, and a source of ignition. The fluid is under pressure, and when the valve is opened and the flint sheds sparks into the mixing fuel/air stream, you get a flame. So, where does the pressure come from, and how much is it?
It turns out that the fluid in the lighter is butane. At standard pressure (1 ata), butane boils at -0.5°C (just under the freezing point of water). The butane in the lighter is not all vapor, however, which means the pressure in the lighter (assuming there's no air in it, just butane liquid and butane vapor) will be the vapor pressure of butane at the ambient temperature of the lighter. At 25°C (about 77°F, or "room temperature"), the vapor pressure of butane is 2.4 ata, or about 20. psi gauge. Of course, the temperature of the site I'd be doing this is 68°F (20°C), so the vapor pressure of butane at that temperature is 2.0 ata. Running through the equations to get the pressure as a depth, the pressure inside the lighter at the ambient temperature of the dive site is equal to the ambient pressure at a depth of about 35 feet (if you do all the math and only round at the end, that is).
Unfortunately, the exercise is to take place at a depth of about 50 feet. At that depth, if you pressed the valve button on the lighter (assuming it hadn't been crushed), air would flow *into* the fuel reservoir. Obviously, the lighter will not light in that situation.
So, the question is simple: If you had a small "airquarium" 50 feet below the surface, and you wanted to light a candle that is stuck in a cupcake inside that small container, how would you light it?
All in the name of science, of course. :biggrin:
- It must be cake.
- It must have candles.
- The candles must be lit.
The first corollary to the third requirement, then, was obvious. The candles would require a gaseous atmosphere capable of sustaining combustion -- in short, air. Various issues immediately follow from that. First, some container must be procured to hold the air. The larger the volume of the container, the more weight will be required to offset its buoyancy. In order to reduce the problem to manageable scale, the container needs to be of relatively small volume -- an 8-pound block of lead (the largest single block I have handy) will offset a gallon of air, so that's about the size of it.
Of course, by limiting the volume of the container, we encounter other issues. Perhaps most significant of these is the oxygen consumption of the candles (as well as the heat generation which is the direct result of said consumption). Upon further thought, we consider the case of the one-year-old child. Said child's birthday cake is adorned with but a single candle, and yet, it is in no way found lacking in birthday-cake-ness. With that in mind, reducing the number of candles to a single representative candle should not invalidate the procedure, and it significantly reduces the oxygen consumption and heat generation parameters versus multiple candles.
On a similar note, the physical size of the cake has not been shown to be of particular importance. In fact, the size of the cake is almost always a function of the size of the guest list, a parameter which has no defined correlation to the number of candles (or any parameter from which the number of candles is derived). Therefore, as long as the cake-ness requirement is satisfied and there is sufficient material to anchor the sole candle, the dimensions are unimportant. While several fractional sheet cakes are often cut from a single full-sheet cake, continuing that to the point of frosting a single piece of cake would seem disingenuous, however, using one intact cupcake does not have the same stigma. (There is also a body of evidence indicating that the cupcake approach has significant force of tradition behind it, even if less than that of the full birthday cake concept.)
So, now we've defined the scope of the project to:
- One container of air.
- One cupcake.
- One candle.
- A method of lighting the candle.
What is a disposable lighter, anyway? Well, at its simplest, it is a container of flammable fluid, a valve, and a source of ignition. The fluid is under pressure, and when the valve is opened and the flint sheds sparks into the mixing fuel/air stream, you get a flame. So, where does the pressure come from, and how much is it?
It turns out that the fluid in the lighter is butane. At standard pressure (1 ata), butane boils at -0.5°C (just under the freezing point of water). The butane in the lighter is not all vapor, however, which means the pressure in the lighter (assuming there's no air in it, just butane liquid and butane vapor) will be the vapor pressure of butane at the ambient temperature of the lighter. At 25°C (about 77°F, or "room temperature"), the vapor pressure of butane is 2.4 ata, or about 20. psi gauge. Of course, the temperature of the site I'd be doing this is 68°F (20°C), so the vapor pressure of butane at that temperature is 2.0 ata. Running through the equations to get the pressure as a depth, the pressure inside the lighter at the ambient temperature of the dive site is equal to the ambient pressure at a depth of about 35 feet (if you do all the math and only round at the end, that is).
Unfortunately, the exercise is to take place at a depth of about 50 feet. At that depth, if you pressed the valve button on the lighter (assuming it hadn't been crushed), air would flow *into* the fuel reservoir. Obviously, the lighter will not light in that situation.
So, the question is simple: If you had a small "airquarium" 50 feet below the surface, and you wanted to light a candle that is stuck in a cupcake inside that small container, how would you light it?
All in the name of science, of course. :biggrin:
)
