A mountaineer is climbing a very tall mountain. She has bottled oxygen (oxygen gas in a rigid, metal cylinder) with her, and she breathes the oxygen on the ascent. At the summit, she stops breathing the bottled oxygen and descends safely to the base of the mountain. The temperature on the summit is –15°C, and the temperature at the base is 20°C. Describe how the change in temperature and the change in the amount of gas in the oxygen cylinder affect the pressure of the gas inside the cylinder during the ascent and descent of the mountain

When the temperature and the amount of gas decrease, the pressure decreases.

Explanation:

At the base of the mountain, the temperature is 20 °C (293 K) and as she climbs, the temperature on the summit decreases to -15 °C (258 K). We can see the effect of the temperature on the pressure using Gay-Lussac's law.

P/T = k

P = k × T

As we can see, there is a direct relationship between P and T. So, when the temperature decreases, the kinetic energy of the gas does as well, and consequently, the pressure decreases.

Also, as the mountaineer consumes oxygen, the number of moles (n) of oxygen decreases. We can appreciate the effect on the pressure using the gas ideal equation.

P × V = n × R × T

P = n × R × T / V

There is also a direct relationship between n and P. When the amount of gas decreases, so does the pressure.

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