There is a small amount of water at the bottom of a sealed containerof volume 4.3 liters which is otherwise full of an ideal gas. A thin tube open to the atmosphere extends down into the water, and up to a height of 238 cm. The system is initially a pressure that maintains a column of water that just reaches the top of the tube, and at temperature 149 Celsius.
If we increase the temperature of the gas until .67 liters of water have exited at the top of the tube, then what is the temperature?
To solve this problem, we need to use the ideal gas law equation:
PV = nRT
Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of gas
- R is the ideal gas constant
- T is the temperature of the gas
First, we need to calculate the initial number of moles of gas in the container. Since we have an ideal gas and know the initial pressure and volume, we can rearrange the ideal gas law equation to solve for n:
n = PV / RT
Given that the initial volume is 4.3 liters, the pressure is the pressure to maintain a column of water that just reaches the top of the tube, and the temperature is 149 Celsius (which needs to be converted to Kelvin), we can substitute these values into the equation to find the initial number of moles.
Next, we need to calculate the final pressure. Since a certain volume of water has exited the container, the volume of the gas will decrease. We can find the final volume of the gas by subtracting the volume of the water that has exited from the initial volume.
Now, we can rearrange the ideal gas law equation to solve for the final temperature:
T = PV / nR
Substituting the final pressure, final volume, initial number of moles, and the ideal gas constant into the equation will give us the final temperature.
By following these steps, we can determine the final temperature of the gas after .67 liters of water have exited at the top of the tube.