How Does Changing Gas Quantity and Temperature Affect Pressure?

[Alethia]

Hi, I'm having some trouble doing my homework for Physics. I would appreciate it if anybody would help me or lead me in the right direction. Thank you.

1. Gas is confined in a tank at a pressure of 1.0x18^8 Pa and a temperature of 15.0 degrees Celcius. If half the gas is withdrawm and the temperature is raised to 65.0 degrees Celcius, what is the new pressure in the tank in Pa?
---Normally for problems such as these, I use the prportion of (P1V1)/T1 = (P2V2)/T2. But I don't know how to solve without the volume. Is there a way I couild find the volume, or do I have to use a different forumla?

2. A 5450-m^3 blimp circles Fenway Park duing the World Series, suspended in the Earth's 1.21-kg/m^3 atmosphere. The density of the helium in the blimp is 0.178 kg/m^3. A) What is the buoyant force that suspends the blimp in the air? B) How does this buotant force compare to the blimp's weight? c) How much weight, in addition to the helium, can the blimp carry and still continue to maintain a constant altitude?
---I solved for a and for the answer 9.5x10^3 N by using the boyant force formula = D*g*v. However, I don't know what to do on b and c.


3. Allegra's favorite ride at the Barrel-O-Fun Amusement Park is the Flying Umbrella, which is lifted by a hydraulic jack. The operator activates the ride by applying a forcce of 72 N to a 3.0-cm-wide cylindrical piston, which holds the 20000. N ride off the ground. What is the diameter of the piston that holds the ride?
---Well honestly, for this problem, I have no idea where to start or do. n_n


Thank you! Anything helps and is appreciated.

 

[Janitor]

Re part 1 of your question

Since the tank is presumably rigid, its volume is constant. So can't you just use P1/(N1T1) = P2/(N2T2) where N2=1/2 N1? And of course, don't forget to convert to absolute temperature when doing the ratio.

So P2 = (1/2) P1T2/T1.

 

[Janitor]

Re part 3

The essential idea is that pressure is constant throughout the hydraulics. So you have P = F1/A1 = F2/A2. So A2=A1F2/F1. Let A1=3 cm, F1=72 N, F2=20,000 N. Then it's just D2=2 square root (A2/pi).

 

[Doc Al]

Originally posted by Alethia
1. ...
---Normally for problems such as these, I use the prportion of (P1V1)/T1 = (P2V2)/T2. But I don't know how to solve without the volume. Is there a way I couild find the volume, or do I have to use a different forumla?

As Janitor points out, the volume is constant. But you can't just use P1/T1 = P2/T2. That's only true if the amount of gas (number of molecules) was fixed, which is not the case here. Use the entire ideal gas law, putting everything that's constant on one side. Then you can set up the right proportions.

2. ...
---I solved for a and for the answer 9.5x10^3 N by using the boyant force formula = D*g*v. However, I don't know what to do on b and c.

For b, if the thing is floating it must be in equilibrium. What does that mean? For c, realize that the bouyant force must be greater that just the weight of the helium---otherwise what's the point? You wouldn't be able to lift anything but the helium.

3. ...
---Well honestly, for this problem, I have no idea where to start or do.

For hydraulic jacks, realize that the pressure in the fluid is the same on both sides. Find the pressure on one side, then use that information to figure out how wide the other piston must be. (Set it up as a ratio.)

 

[Alethia]

Okay for number 1 I calculated it, and I ended up with 5.7x10^7 Pa. Is that right?

Uhm, if it is in equilibrium it is at zero. So does that mean that the boyant force cancels with the blimp's weight? And for c, yeah, it would make sense that the buoyant force is larger... but how would I calculate it?

On the last problem, why is A1 = 3 cm? And how did you conclude it to this: D2=2 square root (A2/pi)? I'm sorry, but could you break it down a little more?

Thank you both! Much appreciated!

 

[Janitor]

My goof.

When I was writing up some hints on Q 3, I was thinking the area of the cylinder bore was 3 square centimeters, but I see that in fact the diameter was 3 cm. My mistake, sorry. Anyway, since A = pi r^2, then A = pi (D/2)^2. Inverting this, D = 2 square root (A/pi).

 

[Janitor]

As far as the numerical answer to Q 1 goes, did you add 273 to each Celsius temperature to get it into Kelvins? If so, then you are probably okay. I don't have a calculator handy. When you wrote " 1.0x18^8 Pa" did you mean 1.0x10^8 Pa?

 

[Alethia]

Originally posted by Janitor
As far as the numerical answer to Q 1 goes, did you add 273 to each Celsius temperature to get it into Kelvins? If so, then you are probably okay. I don't have a calculator handy. When you wrote " 1.0x18^8 Pa" did you mean 1.0x10^8 Pa?

Yeah I meant x10^8. Whoopos. =) And yes, I did convert everything to Kelvins.

 

[Alethia]

Originally posted by Janitor
When I was writing up some hints on Q 3, I was thinking the area of the cylinder bore was 3 square centimeters, but I see that in fact the diameter was 3 cm. My mistake, sorry. Anyway, since A = pi r^2, then A = pi (D/2)^2. Inverting this, D = 2 square root (A/pi).

Oh! Thank you! I calculated it and it came out as 50 cm even. =) Thanks!

 

[Doc Al]

Originally posted by Alethia
Uhm, if it is in equilibrium it is at zero. So does that mean that the boyant force cancels with the blimp's weight? And for c, yeah, it would make sense that the buoyant force is larger... but how would I calculate it?

For B: Yes, the bouyant force equals the total weight of the blimp.
For C: Calculate the weight of the helium (using density and volume) and subtract that from the total weight (which equals the bouyant force).

 

[GCT]

1. Gas is confined in a tank at a pressure of 1.0x18^8 Pa and a temperature of 15.0 degrees Celcius. If half the gas is withdrawm and the temperature is raised to 65.0 degrees Celcius, what is the new pressure in the tank in Pa?

Withdrawing half of the gas will half the pressure. Raising the temperature by ? percent (figure it out yourself, in kelvins) will raise the pressure by the same percent.