Answer :
Final answer:
After compressing a gas from a volume of 22.4 liters to 6.2 liters at a constant temperature, the new pressure of the gas is roughly 3.61 atmospheres. This is derived using Boyle's Law, which dictates the inverse relationship between the pressure and volume of a gas at a constant temperature.
Explanation:
From the information given in the question, you are asked to calculate the new pressure of a gas after it's compressed from a volume of 22.4 liters to 6.2 liters at a constant temperature. This situation involves the application of Boyle's Law in Physics, which states that at a constant temperature, the volume of a gas is inversely proportional to its pressure.
Boyle's law is mathematically expressed as P1*V1 = P2*V2 where P1 and V1 represent the initial pressure and volume respectively, and P2 and V2 represent the final pressure and volume.
In your case, P1 = 1 atmosphere (the initial pressure), V1 = 22.4 liters (the initial volume), and V2 = 6.2 liters (the final volume). Substituting these values into the equation, you can solve for P2 (final pressure) like this:
1 atmosphere * 22.4 liters = P2 * 6.2 liters, hence P2 = (1 atmosphere * 22.4 liters) / 6.2 liters. So, the new pressure of the gas after it has been compressed is about 3.61 atmospheres.
Learn more about Boyle's Law here:
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Hello!
The answer is: The new pressure of the gas is 3.6 atm.
Why?
From the statement we know that the gas is kept at a constant temperature of 0°C, so, if the gas keeps a constant temperature we can use the Boyle's Law to solve this problem.
The Boyle's Law states that:
[tex]P_{1}V_{1}=P_{2}V_{2}[/tex]
Where,
P is the pressure of the gas.
V is the volume of the gas.
So, the given information is:
[tex]V_{1}=22.4L\\P_{1}=1atm\\V_{2}=6.2L[/tex]
Now, substituting it into the Boyle's Law equation to calculate the new pressure, we have:
[tex]P_{1}V_{1}=P_{2}V_{2}\\\\1atm*22.4L=P_{2}*6.2L\\\\P_{2}=\frac{1atm*22.4L}{6.2L}=3.6atm[/tex]
So, the new pressure is 3.6 atm.
Have a nice day!
