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Hikers have noticed that a sealed bag of potato chips puffs up when taken to the top of a mountain. Suppose that at the valley floor below, the air pressure is 1. 0 atm, temperature is 25°C, and the volume of the chip bag is 0. 985 L. At the top of the mountain, the temperature is 22°C and the chip bag has puffed up to 1. 030 L. What is the air pressure on top of the mountain? atm.

Respuesta :

The final pressure of the air at the top of the mountain has been 0.818 atm.

The gas in the sealed potato bag has been assumed to be the ideal gas.

Since, there has been no change in the moles of gas, the relationship of initial temperature, pressure, and volume, and final units has been given as:

[tex]\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}[/tex]

Computation for the air pressure at top of mountain

The units at valley floor has been considered as initial units, while at the top of mountain are considered as final units.

  • The pressure at valley floor, [tex]P_1=1\;\rm atm[/tex]
  • The temperature at the valley floor, [tex]T_1=25^\circ \rm C[/tex]
  • The volume at the valley floor, [tex]V_1=0.985\;\rm L[/tex]
  • The temperature at the top of the mountain, [tex]T_2=22^\circ \rm C[/tex]
  • The final volume at the top of the mountain, [tex]V_2=1.03\;\rm L[/tex]

Substituting the values for the final pressure of the potato chips puff at the top of the mountain, [tex]P_2[/tex]

[tex]\rm \dfrac{1\;atm\;\times\;0.985\;L}{25^\circ C} =\dfrac{\textit P_2\;\times\;1.030\;L}{22^\circ C} \\\\0.03832=0.0468\;\textit P_2\\\\\textit P_2=0.818\;atm[/tex]

The final pressure of the air at the top of the mountain has been 0.818 atm.

Learn more about pressure, here:

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