The problem you have uploaded involves a gas cylinder containing nitrogen gas under pressure, and we are tasked with determining the final volume of gas after it is allowed to escape. Here’s how we can solve it:

Given:

• Diameter of the cylinder: 3.6 cm (radius = 1.8 cm)
• Height of the cylinder: 14 cm
• Gas pressure inside the cylinder: 20.4 atm

We can use the ideal gas law and the formula for the volume of a cylinder to solve this.

First, let's calculate the volume of the cylinder using the formula: $V = \pi r^2 h$ where:

• $r = 1.8 \, \text{cm} = 0.018 \, \text{m}$ (radius in meters),
• $h = 14 \, \text{cm} = 0.14 \, \text{m}$,
• $\pi \approx 3.1416$.

Then, we need to apply the gas laws to figure out how much gas will escape. Since the gas is initially at 20.4 atm and expands to atmospheric pressure (which is 1 atm), the volume at the end can be found using: $P_1 V_1 = P_2 V_2$ where:

• $P_1 = 20.4 \, \text{atm}$,
• $V_1$ is the volume of the cylinder (which we’ll calculate),
• $P_2 = 1 \, \text{atm}$,
• $V_2$ is the final volume (the unknown).

Let me calculate this step-by-step.### Calculations:

1. Volume of the cylinder: $0.0001425 \, \text{m}^3$ (or $142.5 \, \text{cm}^3$).
2. Final volume of nitrogen gas at 1 atm: $2.91 \, \text{liters}$.

So, after the gas escapes and expands to atmospheric pressure, the total volume of nitrogen gas is 2.91 liters.

Would you like a detailed breakdown of any step or further clarifications?

Here are some related questions you might find helpful:

1. How does the ideal gas law apply to different gas types?
2. What assumptions are made when using the ideal gas law?
3. How would the result differ if the temperature changed during the expansion?
4. How is pressure in atmospheres converted to other units (e.g., Pascals)?
5. What is the significance of significant digits in scientific calculations?

Tip: Always make sure to convert units consistently, especially when dealing with different measurement systems like meters and centimeters.