Question

The planet Jupiter has a surface temperature of \(140 \mathrm{~K}\) and a mass 318 times that of Earth. Mercury (the planet) has a surface temperature between \(600 \mathrm{~K}\) and \(700 \mathrm{~K}\) and a mass 0.05 times that of Earth. On which planet is the atmosphere more likely to obey the ideal-gas law? Explain.

Short answer

Based on the analysis, the atmosphere of Mercury is more likely to obey the ideal gas law compared to Jupiter. Mercury's higher temperature (between 600 K and 700 K) and lower mass (0.05 times Earth's mass) relative to Jupiter (whose temperature is 140 K and has a mass 318 times Earth's mass) make it more likely to meet the conditions necessary for the ideal gas law to be a valid approximation.

Step-by-step solution

1. Jupiter's characteristics

Jupiter has a surface temperature of 140 K and a mass 318 times that of Earth.

2. Mercury's characteristics

Mercury has a surface temperature between 600 K and 700 K, and a mass 0.05 times that of Earth.

3. Comparing temperatures

Jupiter has a lower temperature (140 K) when compared to Mercury's temperature range (600 K - 700 K).

4. Comparing masses

Jupiter has a much larger mass (318 times Earth's mass) compared to Mercury's mass (0.05 times Earth's mass).

5. Analyzing ideal gas law conditions

As stated earlier, the ideal gas law tends to work well when the gas particles have high temperatures and low densities. Since Mercury's temperature is higher than Jupiter's, it indicates that the gas particles on Mercury will have more energetic motion, reducing the significance of any intermolecular attractive forces. Additionally, Jupiter's larger mass implies that it likely has a more dense atmosphere than Mercury, which would lead to more deviations from the ideal gas law due to increased particle interactions.

6. Conclusion:

Based on the analysis, the atmosphere of Mercury is more likely to obey the ideal gas law compared to Jupiter. Mercury's higher temperature and lower mass relative to Jupiter make it more likely to meet the conditions necessary for the ideal gas law to be a valid approximation.