While camping up at Haloooo Mountain (5,500 feet above sea level), it generally takes Sandy about the same amount of time to boil water for her soup as it takes to make a sandwich. This week, Sandy is camping at a trail that is only about 200 feet above sea level. Sandy is very hungry and wants something to eat immediately. Should she make the soup or sandwich? Which would be ready more quickly and why?

Question

anonymous · Answer

She should make the sandwich because it would take more time for the water to boil in the soup. This is according to Gay Lussac's Law, which states that pressure is proportional to temperature. The higher up she goes, the faster it cooks. It would take less time for her to make the sandwich than to make the soup :)

anonymous · Answer

Thanks!

aaronq · Answer

Pressure being proportional to temperature is not the full explanation for a liquid boiling faster. The boiling point of a substance is the temperature where the vapour pressure of the liquid is equal to the atmospheric pressure. At this point, there is a net movement of liquid particles into the gas phase in the gas-liquid equilibrium at the interface (surface). By lowering the atmospheric pressure you lower the temperature necessary to boil a liquid.This means that water won't boil at 100 Celsius but a lower temperature. At 5500 ft the atmospheric pressure is $\approx$620 mmHg$^1$, and the BP of water is 94.37$^2$ celsius. 1. http://www.engineeringtoolbox.com/air-altitude-density-volume-d_195.html 2. http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/vappre.html