Gas Volume Calculation in a Cylindrical Tank

How do we calculate the volume of gas in a cylindrical tank filled with methane gas?

In a cylindrical tank that is 6 inches in diameter and 1.2 meters long, methane gas is filled at a pressure of 80 psig and a temperature of 65°F. How can we determine the amount of methane gas in kilograms present in the tank?

Calculating Gas Volume in a Cylindrical Tank

To calculate the volume of gas in a cylindrical tank filled with methane gas, we need to follow a series of steps:

Step 1: Calculate the volume of the cylindrical tank using its diameter and length.

Step 2: Convert the volume from cubic meters to liters.

Step 3: Convert the pressure from psig to pascals.

Step 4: Convert the temperature from Fahrenheit to Kelvin.

Step 5: Use the ideal gas law equation PV = nRT to calculate the number of moles of methane gas.

Step 6: Convert the number of moles to kilograms using the molar mass of methane gas.

Let's go through each step in detail:

Step 1: The radius of the tank is half of the diameter, so the radius is 6 inches / 2 = 3 inches = 0.0762 meters. The volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height. Plugging in the values, the volume is 0.0277 cubic meters.

Step 2: Converting the volume to liters, we get 27.7 liters.

Step 3: Converting the pressure from psig to pascals, we find it to be 551,580 pascals.

Step 4: Converting the temperature from Fahrenheit to Kelvin, we get 291.48 Kelvin.

Step 5: Using the ideal gas law equation PV = nRT, we calculated the number of moles of methane gas in the tank to be 0.674 moles.

Step 6: Finally, to convert moles to kilograms, we multiply by the molar mass of methane gas to find that there are approximately 0.0108 kilograms of methane gas in the cylindrical tank.