bottle thermometer lab

I've been trying to figure out what went wrong with my bottle thermometer lab. I reviewed the bottle engine notes and the last two homework problems again and they seemed to help." "I think part of the discrepancy in my column height change vs. change in temperature may be my use of a 1-Liter system as opposed to the 3-Liter system used in the online lab. My value was about 3 times the listed value, and I had 1/3 the volume. Since volume and temperature are inversely proportional, this may account for the difference.

As for reasoning out the rest of the problem, I think these are the steps I should have used:

Heating the air in the bottle results in an expansion of the air contained in the bottle. We consider the bottle rigid, so the increased volume of air displaces an equal volume of liquid in the ""exhaust"" tube.

I think I should use work-energy relationships to calculate the distance traveled. I think I should keep the ratio of pressure to temperature constant and calculate the new pressure. I've now got values for the all the state variables except h2, so I can use Bernoulli's equation to solve for it.

p1 = 103000 Pa T1 = 300K and temperature increases to 301 K

pressure therefore increases to 103343 Pa

If I equate `rho * g * h and the difference in pressure , I can solve for h = .0350 m. This is consistent with the approximation of just over a cm in displacement per change in K. This is the vertical distance traveled by the meniscus.

If the tube is perfectly horizontal, can we consider the pressure at each end to be equal, calculate the volume change due to the expansion of gas due to the new temperature and equate that volume to the volume of water displaced in the tube? I think this makes sense because we consider liquid non-compressible.

Thank you for your help with this

Just about everything you say here appears to be compatible with the notes I made within your lab report.

The only exception seems to be the vertical tube, which indicates a pressure increase of about 100 Pa (actually 98 Pa) for each cm of additional height. This is because .01 m * 1000 kg/m^3 * 9.8 m/s^2 = 98 N / m = 98 Pa.