Please could a good heated person solve this physics questions for me.
Thank you.
A scuba tank when full hold 12L of air at 204 atm. Assume an empty tank contains air at 34 atm and is connected to air compressor at the sea level. The air compressor intakes air from the atmosphere , compresses it and then inputs this High pressure in to the scuba tank. If the average flow rate of the air from the atmosphere into the intake port of the air compressor is 290 L/ min, how long will it take to charge the scuba tank? Temperature remains the same as the sorroundings?
P1V1 = P2V2
204*12 = 34*V2
find V2, the volume of the tank, then time = volume/rate
but the volume is the volume at 1 atm, which will be much larger than the tank's volume. So you will need to do a similar calculation with P2 = 1
Sure, I'd be happy to help you with your physics question!
So, we have an empty scuba tank with a starting pressure of 34 atm, and we want to fill it up to 204 atm. We also know the average flow rate of the air into the compressor is 290 L/min.
To find the time it takes to charge the scuba tank, we need to calculate the volume of air we need to add.
The change in pressure, ΔP, is given by:
ΔP = Final pressure - Initial pressure
ΔP = 204 atm - 34 atm
ΔP = 170 atm
Now we need to convert ΔP from atm to liters using Boyle's Law: P1V1 = P2V2
P1V1 = P2V2
34 atm x V1 = 204 atm x (V1 + Vt)
Where Vt is the volume of air we need to fill.
Simplifying the equation, we get:
Vt = (34 atm x V1) / (204 atm - 34 atm)
Vt = (34 atm x V1) / 170 atm
Vt = 0.2 x V1
Now, we can substitute the value of V1. Since the empty tank holds 12L of air, the volume of air we need to add is:
Vt = 0.2 x 12L
Vt = 2.4L
So, we need to add 2.4L of air to the scuba tank.
Knowing that the average flow rate of the air into the compressor is 290 L/min, we can find the time it takes to charge the tank by dividing the volume of air we need to add by the flow rate:
Time = Volume / Flow rate
Time = 2.4L / (290 L/min)
Calculating this, we find:
Time ≈ 0.008276 minutes
So, it will take approximately 0.008276 minutes to charge the scuba tank.
Hope that helps! Let me know if you have any more questions or if there's anything else I can clownishly clarify for you!
To solve this problem, we can use Boyle's Law and the formula for flow rate.
1. Boyle's Law states that the pressure of a gas is inversely proportional to its volume, assuming the temperature remains constant. Mathematically, it can be expressed as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
2. Given that the scuba tank holds 12L of air at 204 atm when full and starts with 34 atm, we can set up the equation as (34 atm)(V1) = (204 atm)(12L), where V1 is the initial volume of air in liters.
3. Solving for V1, we find that V1 = (204 atm)(12L)/(34 atm) = 72L.
4. Now, we can find the difference in volume that needs to be filled by the air compressor: ΔV = 12L - 72L = -60L.
5. The flow rate of the air into the air compressor is given as 290 L/min.
6. To find the time it takes to charge the scuba tank, we use the formula: time = volume / flow rate. Plugging in the values, we have time = (-60L) / (290 L/min).
7. The unit of Liters cancels out, and we are left with time = -60 / 290 min.
8. Finally, we can calculate the time it takes to charge the scuba tank, which is approximately 0.21 min or 12.5 seconds.
Therefore, it will take approximately 12.5 seconds to charge the scuba tank.
To find out how long it will take to charge the scuba tank, we need to determine the volume of air that needs to be added to the tank and then divide that by the average flow rate of the air compressor.
First, let's find the difference in pressure between the initial pressure and the final pressure in the tank:
Pressure difference = Final pressure - Initial pressure
Final pressure in the scuba tank = 204 atm
Initial pressure in the empty tank = 34 atm
Pressure difference = 204 atm - 34 atm = 170 atm
Next, let's convert the pressure difference to the same units as the flow rate:
Pressure difference = 170 atm * (101.325 kPa/atm) = 17234.25 kPa
Now, let's convert the volume of air to the same units as the flow rate:
Volume of air = 12 L = 12 L * (1000 cm³/1 L) = 12000 cm³
Since the given flow rate is in L/min, let's convert the flow rate to cm³/min:
Flow rate = 290 L/min = 290 L * (1000 cm³/1 L) = 290000 cm³/min
Now, we can calculate the time it will take to charge the scuba tank:
Time = Volume of air / Flow rate
Time = 12000 cm³ / 290000 cm³/min
Time = 0.04138 min
Therefore, it will take approximately 0.04138 minutes (or approximately 2.48 seconds) to charge the scuba tank.