Chapter 4: Problem 17

If the Earth's atmosphere warmed up and expanded to a larger total volume but its total mass did not change, would this affect the atmospheric pressure at sea level? Would this affect the pressure at the top of Mount Everest? Explain.

Short Answer

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Based on the step-by-step solution provided, create a short answer: As the Earth's atmosphere warms up and expands, the atmospheric pressure at sea level decreases due to the lower air density and weight of the air column. While at the top of Mount Everest, the pressure would experience a slight increase, as the pressure difference between sea level and the top of the mountain would be smaller due to the change in density.

Step by step solution

Understand the Ideal Gas Law and Atmospheric Pressure

The Ideal Gas Law states: PV=nRT, where P is the pressure, V is the volume, n is the number of moles of gas particles, R is the gas constant and T is the temperature. Atmospheric pressure is the force exerted by the weight of the air above a given point, proportional to the density and height of the air column.

Analyze the warming and expansion effect on atmospheric pressure at sea level

When the atmosphere warms up, its total volume will increase (V becomes larger). However, its total mass does not change, which means the number of gas particles (n) remains constant. We can rearrange the Ideal Gas Law equation to isolate the pressure: P = (nRT) / V. Since n, R, and T increase while V also increases due to the warming of the atmosphere, the overall effect on pressure (P) at sea level is unclear. We need to take into consideration that the density of air decreases with expansion.

Consider the effect of air density

As the atmosphere expands, the air density decreases, meaning its weight per unit volume decreases as well. Since atmospheric pressure is determined by the weight of the air column, it would decrease at sea level.

Explain the impact on pressure at the top of Mount Everest

At the top of Mount Everest, the pressure is lower than at sea level due to the smaller air column above it. With the warming and expanding of the atmosphere, the pressure decrease from sea level to the top of Mount Everest is expected to be smaller. The air density decreases with expansion, and thus the pressure decrease rate as we go higher would also be less. The atmospheric pressure at the top of Mount Everest would increase, though the increase might be minimal.

Conclusion

As the Earth's atmosphere warms up and expands to a larger total volume without changing its total mass, the atmospheric pressure at sea level would decrease due to the lower air density and weight of the air column. The pressure at the top of Mount Everest would be affected too, and it would experience a slight increase in pressure, as the pressure difference between sea level and top of Mount Everest would be smaller due to the change in density.

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If the Earth's atmosphere warmed up and expanded to a larger total volume but its total mass did not change, would this affect the atmospheric pressure at sea level? Would this affect the pressure at the top of Mount Everest? Explain.

Short Answer

Step by step solution

Understand the Ideal Gas Law and Atmospheric Pressure

Analyze the warming and expansion effect on atmospheric pressure at sea level

Consider the effect of air density

Explain the impact on pressure at the top of Mount Everest

Conclusion

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