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Difficulty: HardDrawing Valid Inferences

Spectroscopic analysis of the exoplanet K2-315b has confirmed the concurrent presence of both atmospheric methane and water vapor. According to atmospheric circulation models, whenever an exoplanet contains both methane and water vapor in its atmosphere, high-altitude silicate cloud decks inevitably form. Furthermore, such silicate cloud decks can form only if the planet's equilibrium temperature remains below 600 K600\text{ K} and its upper-atmosphere wind speeds exceed 150 m/s150\text{ m/s}. Finally, all exoplanets with equilibrium temperatures below 600 K600\text{ K} undergo significant atmospheric hydrogen retention.

If the statements above are true, which of the following must also be true regarding K2-315b?

  1. A
    High-altitude silicate cloud decks can form on an exoplanet only if both atmospheric methane and water vapor are present.
  2. B
    Any exoplanet with upper-atmosphere wind speeds exceeding 150 m/s150\text{ m/s} will undergo atmospheric hydrogen retention.
  3. K2-315b undergoes significant atmospheric hydrogen retention.Answer
  4. D
    K2-315b's equilibrium temperature is greater than or equal to 600 K600\text{ K}.
  5. E
    The presence of water vapor on K2-315b is the primary cause of its high upper-atmosphere wind speeds.

Answer

K2-315b undergoes significant atmospheric hydrogen retention.
The passage establishes a chain of formal conditions. First, K2-315b has both methane and water vapor. Second, whenever both gases are present, silicate cloud decks form. Therefore, K2-315b has silicate cloud decks. Third, silicate cloud decks can form only if the equilibrium temperature is below 600 K600\text{ K}. Since cloud decks exist on K2-315b, its temperature must be below 600 K600\text{ K}. Fourth, any planet with a temperature below 600 K600\text{ K} undergoes atmospheric hydrogen retention. Consequently, it must be true that K2-315b undergoes significant atmospheric hydrogen retention.

Step-by-Step Solution

1
Identify the initial factual premise about K2-315b
K2-315b possesses both atmospheric methane and water vapor.
This establishes the starting point for applying the conditional statements.
2
Apply the sufficient condition rule for cloud formation
High-altitude silicate cloud decks must form on K2-315b.
The passage states that the joint presence of methane and water vapor inevitably leads to silicate cloud deck formation.
3
Apply the necessary condition rule for cloud deck existence
K2-315b's equilibrium temperature is below 600 K600\text{ K} (and its wind speeds exceed 150 m/s150\text{ m/s}).
Cloud decks can form only if the temperature is below 600 K600\text{ K}. Since cloud decks form, the temperature condition must be satisfied.
4
Apply the final rule regarding temperature and hydrogen retention
K2-315b undergoes significant atmospheric hydrogen retention.
All exoplanets with equilibrium temperatures below 600 K600\text{ K} undergo hydrogen retention.

Key Concept

Conditional logic chains and contrapositives
Estimated Time:2m 0s
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Topics

Drawing Valid Inferences

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