For an enclosed gas with a constant temperature, the pressure of the gas changes from 10 atm to 30 atm. What happens to the volume of the gas? a The volume becomes three times its original value. b The volume stays the same as its original value. c The volume becomes one-tenth (1/10) of its original value. d The volume becomes 10 times the original value. e The volume becomes one-third (1/3) of its original value.
According to Boyle's Law, the pressure and volume of an enclosed gas are inversely proportional if the temperature remains constant.
Mathematically, this can be represented as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
In this case, the pressure changes from 10 atm to 30 atm.
Let's substitute the given values into the formula:
(10 atm)(V1) = (30 atm)(V2)
To find the relationship between the initial and final volume, we can simplify the equation:
V1 = (30 atm)(V2) / 10 atm
V1 = 3(V2)
Therefore, the volume becomes three times its original value.
So, the correct answer is (a) The volume becomes three times its original value.
To determine what happens to the volume of the gas when the pressure changes, we can use Boyle's Law. Boyle's Law states that for an enclosed gas at constant temperature, the pressure and volume are inversely proportional.
The mathematical expression for Boyle's Law is:
P1 * V1 = P2 * V2
Where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.
In this case, the initial pressure (P1) is 10 atm and the final pressure (P2) is 30 atm. We want to determine the relationship between the initial volume (V1) and the final volume (V2).
Using Boyle's Law, we can rearrange the equation:
V2 = (P1 * V1) / P2
Substituting the values:
V2 = (10 atm * V1) / 30 atm
Simplifying the equation, we can cancel out the units "atm":
V2 = (V1) / 3
From the equation, we can see that the final volume (V2) is one-third (1/3) of the initial volume (V1).
Therefore, the correct option is e) The volume becomes one-third (1/3) of its original value.
To determine what happens to the volume of the gas, we can use Boyle's law, which states that for an enclosed gas at constant temperature, the product of its pressure and volume is constant.
Mathematically, this can be represented as P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
In this case, the initial pressure (P1) is 10 atm and the final pressure (P2) is 30 atm. Since the temperature is constant, we can solve for V2.
P1 * V1 = P2 * V2
10 atm * V1 = 30 atm * V2
Now, let's solve for V2:
V2 = (10 atm * V1) / 30 atm
V2 = (1/3) * V1
Therefore, the volume of the gas (V2) becomes one-third (1/3) of its original value (V1).
The correct answer is e) The volume becomes one-third (1/3) of its original value.