Consider an ideal gas enclosed within a container with a moveable piston and a valve through which additional ideal gas can be added to the container. Which one of the following actions may not result in an increase in pressure?

Increase the temperature, the volume, and the number of moles of gas in the container.

Increase the temperature of the gas, while keeping its volume and number of moles inside the container constant.

Decrease the volume, while keeping the temperature and the number of moles of gas in the container constant.

Decrease the volume while increasing the temperature and keep the number of moles inside the container constant.

Increase the number of moles of gas inside the container, while keeping the temperature and volume constant.

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What might happen if you increased the volume?

To determine which action may not result in an increase in pressure, we need to consider the ideal gas law, which states that:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.

Let's go through each option and analyze the effect on pressure:

1. Increase the temperature, the volume, and the number of moles of gas in the container:
- Increasing the temperature (T) will increase the pressure (P) according to the ideal gas law.
- Increasing the volume (V) will decrease the pressure (P) according to Boyle's Law (assuming the temperature and number of moles are constant).
- Increasing the number of moles (n) will increase the pressure (P) according to the ideal gas law.

Since both increasing the temperature and the number of moles result in an increase in pressure, and increasing the volume decreases the pressure, this option will result in an increase in pressure.

2. Increase the temperature of the gas, while keeping its volume and number of moles inside the container constant:
- Increasing the temperature (T) will increase the pressure (P) according to the ideal gas law.
- Keeping the volume (V) and the number of moles (n) constant will not affect the pressure.

Since increasing the temperature will increase the pressure, this option will result in an increase in pressure.

3. Decrease the volume, while keeping the temperature and the number of moles of gas in the container constant:
- Decreasing the volume (V) will increase the pressure (P) according to Boyle's Law.
- Keeping the temperature (T) and the number of moles (n) constant will not affect the pressure.

Since decreasing the volume will increase the pressure, this option will result in an increase in pressure.

4. Decrease the volume while increasing the temperature and keep the number of moles inside the container constant:
- Decreasing the volume (V) will increase the pressure (P) according to Boyle's Law.
- Increasing the temperature (T) will further increase the pressure (P) according to the ideal gas law.
- Keeping the number of moles (n) constant will not affect the pressure.

Since both decreasing the volume and increasing the temperature result in an increase in pressure, this option will result in an increase in pressure.

5. Increase the number of moles of gas inside the container, while keeping the temperature and volume constant:
- Increasing the number of moles (n) will increase the pressure (P) according to the ideal gas law.
- Keeping the temperature (T) and the volume (V) constant will not affect the pressure.

Since increasing the number of moles will increase the pressure, this option will result in an increase in pressure.

From the analysis, options 1, 2, 3, 4, and 5 will all result in an increase in pressure. Therefore, none of the given actions may not result in an increase in pressure.