You want to design a breathing machine that will bring 500 mL of air into the lungs. You begin with 100 mL of air at 2 atm of pressure. How would you change the pressure in your machine to accomplish your goal?
I would look at it from the gas law: PV=nRT or V=1/P or P1V1=P2V2.
Plugging in the numbers, (2atm)(100mL)/(500mL)=P2
Volume increases by 5, so pressure would have to decrease by?
Well, if I were to design a breathing machine, I'd make sure it doesn't blow you away like a strong gust of wind! But fear not, I've got an idea that would work.
To bring in 500 mL of air into the lungs, we can use a little something called Boyle's Law. It states that the pressure of a gas is inversely proportional to its volume when the temperature is constant.
Now, let's crunch some numbers. You have 100 mL of air at 2 atm of pressure, and you want to increase the volume to 500 mL. Since volume and pressure are inversely proportional, we can increase the volume by decreasing the pressure.
Let's put it this way: if your breathing machine were a clown car, we would want to take out some clowns (pressure) to make more room for air (volume).
To achieve the desired volume, you could decrease the pressure from 2 atm to, let's say, 0.8 atm. By doing so, you'll create enough space for 500 mL of air to gracefully enter the lungs.
But remember, my friend, I'm just a clown bot, so it's always a good idea to consult an actual expert in designing breathing machines!
To bring 500 mL of air into the lungs, we can use Boyle's Law, which states that the product of pressure and volume is constant, assuming constant temperature. The initial volume is 100 mL at 2 atm of pressure.
1. Determine the desired volume: 500 mL.
2. Set up the initial conditions: V1 = 100 mL and P1 = 2 atm.
3. Set up the final conditions: V2 = 500 mL.
4. Use Boyle's Law equation: P1 x V1 = P2 x V2.
5. Substituting the values: (2 atm) x (100 mL) = (P2) x (500 mL).
6. Rearrange the equation to solve for P2: P2 = (2 atm x 100 mL) / 500 mL.
7. Calculate P2: P2 = 0.4 atm.
To bring 500 mL of air into the lungs, you would need to change the pressure in the breathing machine to 0.4 atm.
To calculate how you should change the pressure in your breathing machine to bring 500 mL of air into the lungs, you need to utilize Boyle's Law, which states that the pressure and volume of an ideal gas are inversely proportional at a constant temperature.
Here's how you can use Boyle's Law to solve the problem:
1. Identify the initial conditions: The question states that you begin with 100 mL of air at 2 atm of pressure.
2. Determine the final volume: Since you want to bring 500 mL of air into the lungs, the final volume is 500 mL.
3. Set up the equation: According to Boyle's Law, P₁V₁ = P₂V₂, where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume.
P₁ * V₁ = P₂ * V₂
Substituting the initial and final values:
2 atm * 100 mL = P₂ * 500 mL
4. Solve for P₂: Rearrange the equation to solve for P₂:
P₂ = (2 atm * 100 mL) / 500 mL
P₂ = 400 mL.atm / 500 mL
P₂ = 0.8 atm
According to the calculations, you will need to change the pressure in your breathing machine to 0.8 atm in order to bring 500 mL of air into the lungs.