I wonder… Where would the exhaled helium be created if that spell were used? (Warning: I’ll be taking this way too seriously and I’m fully aware of that.)
It might change cellular respiration, so that instead of CO₂, her mitochondria would produce helium. In that case, would the reaction enthalpy change? Standard enthalpy of formation of CO₂ is -393.5 kJ/mol, but that of He is 0, so the enthalpy of the reaction would be much lower if He were produced, probably leading to immediate starvation on a cellular level (unless, of course, magic solves this problem, but that’s boring, so let’s not consider that).
So, let’s have the CO₂ be replaced in the lungs instead. Mass of He (4 g/mol) is much lower than that of CO₂ (44 g/mol), so, in order to avoid a lot of energy release due to E=mc², we’ll want to replace each molecule of CO₂ with 11 atoms of He (roughly; I won’t go into nucleon binding energies because that should be sufficiently minute an effect). Of course, according to the ideal gas law (pV=nRT), this causes an 11-fold increase in the product of pressure and volume, meaning she either has to exhale very quickly or will suffer something called pulmonary barotrauma, which, according to some quick research, is already a problem to divers if the pressure difference between inside and outside is less than 1 atm.
It would probably be best if the CO₂ replacement occurred very close to the mouth or nose (so that the excess gas can escape rapidly and not cause overpressure). However, and this is crucial, as I understand it, her voice wouldn’t get super-squeaky then, so clearly, this is not an option. It seems that transmuting a small percentage of CO₂ molecules in the lungs (so that the pressure increase would be small enough not to cause barotrauma) and the rest closer to the point of exhalation would be the best course of action.
In summary, when choosing between homework and massively over-analyzing unicorns, I will always choose unicorns.
I wonder… Where would the exhaled helium be created if that spell were used? (Warning: I’ll be taking this way too seriously and I’m fully aware of that.)
It might change cellular respiration, so that instead of CO₂, her mitochondria would produce helium. In that case, would the reaction enthalpy change? Standard enthalpy of formation of CO₂ is -393.5 kJ/mol, but that of He is 0, so the enthalpy of the reaction would be much lower if He were produced, probably leading to immediate starvation on a cellular level (unless, of course, magic solves this problem, but that’s boring, so let’s not consider that).
So, let’s have the CO₂ be replaced in the lungs instead. Mass of He (4 g/mol) is much lower than that of CO₂ (44 g/mol), so, in order to avoid a lot of energy release due to E=mc², we’ll want to replace each molecule of CO₂ with 11 atoms of He (roughly; I won’t go into nucleon binding energies because that should be sufficiently minute an effect). Of course, according to the ideal gas law (pV=nRT), this causes an 11-fold increase in the product of pressure and volume, meaning she either has to exhale very quickly or will suffer something called pulmonary barotrauma, which, according to some quick research, is already a problem to divers if the pressure difference between inside and outside is less than 1 atm.
It would probably be best if the CO₂ replacement occurred very close to the mouth or nose (so that the excess gas can escape rapidly and not cause overpressure). However, and this is crucial, as I understand it, her voice wouldn’t get super-squeaky then, so clearly, this is not an option. It seems that transmuting a small percentage of CO₂ molecules in the lungs (so that the pressure increase would be small enough not to cause barotrauma) and the rest closer to the point of exhalation would be the best course of action.
In summary, when choosing between homework and massively over-analyzing unicorns, I will always choose unicorns.