For this problem, we can apply the ideal gas law relationship in the form of the combined gas law, which relates the initial and final volumes, temperatures, and pressures. The formula is:

$\frac{V_2}{V_1} = \frac{P_1 \cdot T_2}{P_2 \cdot T_1}$

Where:

• $V_1$ is the initial volume (9000 nm³/h)
• $V_2$ is the final volume (which we need to calculate)
• $P_1$ is the initial pressure (1 bar)
• $P_2$ is the final pressure (2 bar)
• $T_1$ is the initial temperature in Kelvin (20°C = 293.15 K)
• $T_2$ is the final temperature in Kelvin (80°C = 353.15 K)

Let's calculate $V_2$.

$V_2 = V_1 \cdot \frac{P_1 \cdot T_2}{P_2 \cdot T_1}$

$V_2 = 9000 \cdot \frac{1 \cdot 353.15}{2 \cdot 293.15}$

I'll compute this for you now.The final volume $V_2$ is approximately 5421.03 nm³/h.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:

1. How does changing the pressure alone affect the volume at constant temperature?
2. What happens to the volume if both temperature and pressure increase proportionally?
3. How is the combined gas law derived from the ideal gas law?
4. How would the calculation change if the initial volume were in different units, such as liters?
5. How do real gases deviate from the ideal gas law at high pressures?

Tip: Always convert temperatures to Kelvin when using gas laws to ensure consistency.