I need help with this question.
1. You have a tank of helium with a volume of 10 liters that is currently under 40 atm of pressure. If you open the valve on the tank and release the helium into a room with a volume of 10,000 liters, how many atmospheres of pressure will the helium now be under? Second, what will happen to the "space" between the helium atoms? Clearly explain your answer, including any assumptions you may need to make in order to answer the question
Since PV is constant, and you have increased the volume by a factor of 1000, the pressure is reduced by a factor of 1000.
To find the new pressure of the helium when released into the room, we can use the principle of conservation of mass and assume an ideal gas behavior.
First, we need to determine the amount of helium in the tank. Since the volume of the tank is given as 10 liters, we assume the tank is initially entirely filled with helium.
Next, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. Mathematically, Boyle's Law is represented as P1V1 = P2V2, where P1 and V1 represent the initial pressure and volume, and P2 and V2 represent the final pressure and volume.
Let's plug in the given values:
P1 = 40 atm (initial pressure)
V1 = 10 liters (initial volume)
V2 = 10,000 liters (final volume)
Using Boyle's Law, we can calculate the final pressure, P2:
P2 = P1 * (V1 / V2)
P2 = 40 atm * (10 liters / 10,000 liters)
P2 = 0.04 atm
Hence, when the helium is released into the room, its pressure will be approximately 0.04 atm.
Now, let's address the second part of the question regarding the "space" between helium atoms. Assuming we are dealing with an ideal gas, the atoms or molecules of helium are considered point masses with negligible volume. Therefore, the "space" between helium atoms will increase as the helium expands into the larger volume of the room.
In other words, the helium atoms will spread out to occupy the available space. This is because gases tend to expand to fill the entire volume available to them. As the helium expands into the room with a significantly larger volume, the average distance between helium atoms will increase, resulting in an increase in the "space" between them.
However, it is important to note that this explanation assumes ideal gas behavior, neglecting any intermolecular forces or atomic/molecular interactions between the helium atoms.