Pikes Peak has an elevation of 4302 m. If a parcel of air at the top of Peaks Peak has a temperature of -17°C and a relative humidity of 85%. If the temperature in Denver (elevation 1609 m) is 18°C the layer of atmosphere between Denver and Pikes Peak is:

Question

Pikes Peak has an elevation of 4302 m. If a parcel of air at the top of Peaks Peak has a temperature of -17°C and a relative humidity of 85%.  If the temperature in Denver (elevation 1609 m) is 18°C the layer of atmosphere between Denver and Pikes Peak is:

BlackTom AI · Accepted Answer

First, restating the problem helps frame the scenario: Pikes Peak is at 4302 m with a parcel of air at the top having T = -17°C and RH = 85%. Denver sits at ~1609 m with T = 18°C. The question asks about the stability of the atmospheric layer between Denver and Pikes Peak.

Option A: Stable. This would imply that the environmental lapse rate is less than the dry adiabatic lapse rate (or otherwise configured so that displaced air sinks back down). If the layer were stable, a parcel rising from Denver toward Peak would cool faster than its surroundings or be cooler than its surroundings at a given height, causing it to sink back. Based on rough numbers below, the estimated environmental lapse rate appears not to support stability, but we will examine all options.

Option B: Unstable. Stability here hinges on comparing the environmental lapse rate (ELR) with the dry adiabatic lapse rate (DALR, about 9.8°C per km). To estimate the ELR between Denver (18°C at ~1.6 km) and Pikes Peak (-17°C at ~4.3 km), compute the temperature difference: -17 - 18 = -35°C, and the height difference: 4.302 km - 1.609 km ≈ 2.693 km. The ELR ≈ -35°C / 2.693 km ≈ -13.0°C per km (i.e., the environment cools by about 13°C per km). Since this ELR is steeper (more cooling with height) than the DALR (~9.8°C/km), a parcel lifted dry-adiabatically would remain warmer than the surrounding air and continue to rise, indicating instability. This reasoning supports the “Unstable” view.

Option C: nuetral. A neutral atmosphere would occur when the ELR equals the DALR (about 9.8°C/km). In this case, the estimated ELR (~13°C/km) does not match 9.8°C/km, so neutrality is not supported by the rough calculation. The mismatch suggests the atmosphere is not in a neutral state.

Option D: No answer text provided. This option represents a placeholder rather than a physical state of the atmosphere. Since the problem provides options that describe stability, dismissing the available physical interpretations as incomplete would not advance understanding. In practice, we still assess the given choices against the physics described above.

Putting the pieces together, your intuition should weigh whether the environmental lapse rate (derived from the data for Denver and Peak) exceeds the dry adiabatic rate. The magnitude suggests the environment cools more rapidly with height than air would if it were rising adiabatically, which typically indicates instability. However, remember that this conclusion rests on a rough calculation using a single vertical segment between two fixed heights and typical lapse-rate values; local variations and moisture can modify the result.

In summary, Option A (Stable) would require a smaller ELR than DALR, which is not what the rough calculation indicates. Option B (Unstable) aligns with an ELR steeper than the DALR, promoting buoyant ascent. Option C (nuetral) would require ELR ≈ DALR, which our estimate does not show. Option D (No answer text provided) is not a physical state of the atmosphere and does not describe stability.

EAS1600 AtmosphericPressure_StabilityHW_2025

Pikes Peak has an elevation of 4302 m. If a parcel of air at the top of Peaks Peak has a temperature of -17°C and a relative humidity of 85%. If the temperature in Denver (elevation 1609 m) is 18°C the layer of atmosphere between Denver and Pikes Peak is:

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类似问题

The atmosphere is typically most unstable _____.

If an atmosphere is stable to convection, it means a rising air parcel will be (choose all correct answers):

Radiative equilibrium temperature profile is stable to convection.

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A conditionally unstable atmosphere is with respect to unsaturated air and with respect to saturated air.

Radiative equilibrium temperature profile is stable to convection.

If the temperature of the air outside the parcel at the summit of Pike Peak is -20°C. What will happen to the parcel when it is released at the summit?

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EAS1600 AtmosphericPressure_StabilityHW_2025

Pikes Peak has an elevation of 4302 m. If a parcel of air at the top of Peaks Peak has a temperature of -17°C and a relative humidity of 85%. If the temperature in Denver (elevation 1609 m) is 18°C the layer of atmosphere between Denver and Pikes Peak is:

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类似问题

The atmosphere is typically most unstable _____.

If an atmosphere is stable to convection, it means a rising air parcel will be (choose all correct answers):

Radiative equilibrium temperature profile is stable to convection.

Radiative equilibrium temperature profile is unstable to convection.

A conditionally unstable atmosphere is ____ with respect to unsaturated air and ____ with respect to saturated air.

Radiative equilibrium temperature profile is stable to convection.

If the temperature of the air outside the parcel at the summit of Pike Peak is -20°C. What will happen to the parcel when it is released at the summit?

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A conditionally unstable atmosphere is with respect to unsaturated air and with respect to saturated air.