Due to accidental mixing of Wyzant questions, you accidentally shoot a dart into the air in a parabolic trajectory which subsequently hits you and injects 80 g of CO2.

Question

Assume that the CO2 immediately assumes your body temperature and standard pressure, thereby inflating your interperitoneal space. None leaks out. In your alarm, you fall backwards into a vat of hand sanitiser, density 0.896 g/mL. If your body volume before beginning this question was 62 L, and your density was 1.05 g/mL, will you float in the hand sanitiser? (Neglect the mass of the dart, it's really the least of your worries.)

Answer 1

The injection history is irrelavant to the problem so no kinematics involved. for our purely thermodynamical senario, well CO2 is not exactly an ideal gas but lets imagine it to be, especially that it is not in a high pressure or low temperature situation.

you have the ideal gas law as: PV=nRT

The molar weight for carbon dioxide is (~12g for C and ~16g for each O so) ~44g therefor 80g is 1.82 mol.

R has the value 8.314 J/(K·mol) or 0.0821 L.atm/(mol·K)., P = 1 atm, K~310K

V= (1.82mol * 0.0821(L.atm/mol.K)*310K)/1atm=46.3 L

well assuming this be added to my puffer-fish body my new volume would become V=108.3L

and my new weight is 80g + 62L * 1.05 kg/L = 65.18 Kg

so my new density would be : 65.18kg/108.3 L= 0.60 Kg/L = 0.60 g/ml

which is significantly less than the hand sanitizer's density. So I would be floating till I .... well LAEK.

And to clarify this is not how physics works in real life but in your imagination universe that's what you should expect.

Disclaimer: No tutor was harmed answering this imaginative, naughty question.