A tire with an inner volume of 0.0250 m3 is filled with air at a gauge pressure of 30.3 psi. If the tire valve is opened to the atmosphere, what volume outside of the tire does the escaping air occupy? Some air remains within the tire occupying the original volume, but now that remaining air is at atmospheric pressure (14.7 psi). Assume the temperature of the air does not change.
m^3
I keep getting .0316m^3 but its wrong I don't know how to do this could someone help please. Thank you.
P1V1=P2V2
P1=30.3+atmpressure
P2= atmpressure
V1=.0250m^3
V2=EscapedV+.0250
put them in, and solve for EscapedV
original pressure = 14.7 + 30.3 = 45 psi
p v = constant
45 * .0250 = 14.7 v
v = .0765
.0765 - .0250 = .0500 m^3
I suspect you used the "gage" pressure. No, bad.
Thank you both of you but both the methods I tried atill am getting it wrong :/...Damon I tried .0500m^3 and that was wrong and Bobpursley I tried your method i got 3.06 m^3 and still that's wrong too I don;t know why. Could someone please help me. Thank you!
Thank you Damon and Bobpursley. I really appreciate it.
To solve this problem, we need to use the ideal gas law, which states:
PV = nRT
Where:
P = pressure (in pascals)
V = volume (in cubic meters)
n = number of moles of gas
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
First, let's convert the given pressures from psi to pascals.
1 psi is equivalent to 6894.76 pascals. So, the gauge pressure of the air in the tire (30.3 psi) is:
30.3 psi * 6894.76 pascals/psi = 209943.828 pascals
Similarly, atmospheric pressure (14.7 psi) is:
14.7 psi * 6894.76 pascals/psi = 101325.372 pascals
Next, we need to find the number of moles of gas in the tire. We can use the ideal gas law to do this. Rearranging the equation gives us:
n = PV / RT
For the initial state when the tire is filled with air, the pressure is 209943.828 pascals, the volume is 0.0250 m^3, and the temperature does not change. The value of R is given as 8.314 J/(mol·K).
n1 = (209943.828 pascals * 0.0250 m^3) / (8.314 J/(mol·K) * T)
Now, let's calculate n1. We can use the fact that the temperature does not change, so T will cancel out in our calculations.
Now, we need to find the final volume of the escaping air. Some of the air remains in the tire and occupies the original volume of 0.0250 m^3. However, this remaining air is now at atmospheric pressure.
Using the ideal gas law again, we can find the final volume:
V2 = n2RT / P2
For the final state when the remaining air is at atmospheric pressure, the pressure is 101325.372 pascals, the number of moles is the same as before, and again, the temperature does not change.
V2 = (n1 * 8.314 J/(mol·K) * T) / 101325.372 pascals
Now, plug in the value of n1 that we calculated earlier (since n1 = n2) and solve for V2.
Once you have found V2, subtract the original volume (0.0250 m^3) to find the volume outside of the tire that the escaping air occupies.
Voutside = V2 - 0.0250 m^3
This will give you the correct answer in cubic meters (m^3).