Chapter 4: Problem 19

If 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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Answer: If Earth's atmosphere warmed up and expanded with constant total mass, the atmospheric pressure at sea level would decrease due to the more significant increase in volume compared to the increase in temperature. The pressure at the top of Mount Everest would also decrease because an even smaller number of air molecules would be present at that altitude, which is due to the expansion of the atmosphere.

Step by step solution

Understand the Ideal Gas Law

The Ideal Gas Law states that PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is temperature (in Kelvin). When the total mass of the atmosphere does not change, the number of moles (n) remains constant as well.

Identify the changes in the atmosphere

In this scenario, the Earth's atmosphere is warming up and expanding. Therefore, we know the temperature (T) is increasing and the volume (V) is also increasing.

Analyze the pressure change at sea level

Since the volume (V) is increasing and the number of moles (n) is constant, we can rearrange the Ideal Gas Law to find the pressure (P): P = nRT / V. As both T and V are increasing, the result of their ratio (T / V) will determine the change in pressure. Due to the large size of Earth's atmosphere, we can assume that the increase in volume (V) would have a more significant effect than the increase in temperature (T). Therefore, the pressure (P) at sea level would decrease.

Analyze the pressure change at the top of Mount Everest

As we move to higher altitudes, the atmospheric pressure decreases due to the decrease in the number of air molecules (n) above that altitude. Thus, the top of Mount Everest already experiences lower pressure compared to sea level. Since the atmosphere is warming up and expanding, the volume (V) at higher altitudes also increases, leading to a further decrease in the pressure at the top of Mount Everest.

Conclusion

If Earth's atmosphere warmed up and expanded to a larger total volume with its total mass remaining constant, the atmospheric pressure at sea level would decrease due to the more significant increase in volume (V) compared to the increase in temperature (T). The pressure at the top of Mount Everest would also decrease as an even smaller number of air molecules would be present at that altitude due to the expansion of the atmosphere.

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If 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

Identify the changes in the atmosphere

Analyze the pressure change at sea level

Analyze the pressure change at the top of Mount Everest

Conclusion

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