To determine which change would cause the greatest increase in pressure, we should consider the ideal gas law, which states that:
\[ PV = nRT \]
Where:
- \( P \) = pressure
- \( V \) = volume (constant in this case)
- \( n \) = number of moles (number of molecules, since we can consider the volume to be constant and thus relevant for a fixed amount of gas)
- \( R \) = ideal gas constant
- \( T \) = temperature in Kelvin
Pressure increases with both the number of molecules (n) and the temperature (T).
Now let's evaluate the provided options:
-
Adding 100 more molecules and decreasing the temperature by 10K:
This adds more molecules (increases \( n \)), but decreasing the temperature (decreases \( T \)) has the opposite effect. The net effect here would likely be a moderate increase in pressure since the increase in molecules may outweigh the temperature drop. -
Releasing 100 molecules and decreasing the temperature by 10K:
This decreases both the number of molecules (decreases \( n \)) and the temperature, leading to a decrease in pressure. -
Releasing 100 molecules and increasing the temperature by 10K:
This decreases the number of molecules (decreases \( n \)), but increases the temperature. However, the decrease in molecules will have a dominant effect, leading to a decrease in pressure. -
Adding 100 more molecules and increasing the temperature by 10K:
This adds more molecules (increases \( n \)) and increases the temperature (increases \( T \)), which would lead to a significant increase in pressure.
Comparing the options:
- The first option theoretically could increase pressure, but the temperature decrease would limit that increase.
- The second and third options decrease pressure.
- The fourth option (adding more molecules and increasing temperature) will result in the greatest increase in pressure overall.
Therefore, the answer is:
Adding 100 more molecules and increasing the temperature by 10K.