To determine which change would cause the greatest increase in pressure in an airtight bucket with a constant volume, we can use the ideal gas law, which states that \( P = \frac{nRT}{V} \), where \( P \) is pressure, \( n \) is the number of moles (which is directly proportional to the number of molecules), \( R \) is the ideal gas constant, \( T \) is the temperature in Kelvin, and \( V \) is the volume.
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Adding 100 more molecules and decreasing the temperature by 10K: This would increase the number of molecules (which increases pressure), but decreasing the temperature would reduce pressure.
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Adding 100 more molecules and increasing the temperature by 10K: This increases both the number of molecules and the temperature, which would result in a significant increase in pressure.
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Releasing 100 molecules and increasing the temperature by 10K: This reduces the number of molecules (which decreases pressure) but increases the temperature (which increases pressure). The net effect would likely be a decrease in pressure.
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Releasing 100 molecules and decreasing the temperature by 10K: Both changes (decreasing the number of molecules and decreasing the temperature) would contribute to a decrease in pressure.
Comparing these scenarios, the second option—adding 100 more molecules and increasing the temperature by 10K—results in an increase in both the number of molecules and the temperature, likely causing the greatest increase in pressure.
Therefore, the best answer is:
Adding 100 more molecules and increasing the temperature by 10K.