How Does Pressure and Volume Change in a Gas Cylinder?

[metalmagik]

Homework Statement

Problem comes straight from a 2001 AP Physics B test
http://img151.imageshack.us/img151/6159/physicscylinderszq4.png

Homework Equations

PV = nRT

KE = 3/2KT

deltaU = Q+W

The Attempt at a Solution

Okay, for the first two (a and b) I arrived at an answer of double the initial pressure of State 1 and half of the initial volume of State 1. This was because after I drew myself a little P vs. V graph, I knew the two States had to be on the same isotherm, so pressure had to increase in order for volume to decrease. Also, I just realized as I write this, if T is constant, in PV = nRT that means nRT is a constant and as P increases, V must decrease.
I'm pretty sure that's right, if it's wrong, I would appreciate clarification.

For c I got Isobaric, simply because isothermal and adiabatic do not work.

For d I got Yes, 4 --> 1 is isobaric simply because I drew a P versus V graph and since it has to go back to the same isotherm State 2 was on, but volume had to decrease, it had to be isobaric.

I do not understand e. I'm having a hardtime knowing what the weight does...do you have to use P = F/A?

Thanks for any help at all on this, any corrections if I am wrong and any elaboration on any topic is greatly appreciated.

 

[anathema]

Hello! It looks like you have a good understanding of the problem so far. Your reasoning for parts a and b is correct - the pressure must increase and the volume must decrease in order to stay on the same isotherm. For part c, your answer of isobaric is correct. Remember, isobaric means constant pressure, so since the pressure is not changing in this case, it must be isobaric.

For part d, your reasoning is also correct. Since the volume must decrease in order to stay on the same isotherm, the process must be isobaric.

For part e, you are correct in thinking that you can use P = F/A. In this case, the weight is acting as a force on the piston, and you can use the equation P = F/A to calculate the pressure at the bottom of the cylinder. This pressure will then be used in the PV = nRT equation to solve for the final volume.

Overall, it seems like you have a good understanding of the problem and have used the correct equations and reasoning to arrive at your solutions. Great job!

 

[m2003]

I would like to provide some feedback on your solution attempt. Your reasoning for a and b seems correct, as the states must be on the same isotherm and the ideal gas law equation shows that as pressure increases, volume must decrease. However, it would be helpful if you showed your calculations and units to ensure accuracy.

For c, your reasoning for choosing isobaric is not entirely clear. It would be helpful to explain why the other two options, isothermal and adiabatic, do not work.

For d, your reasoning for choosing isobaric also seems correct, but again, it would be helpful to see your calculations and units.

For e, the weight does not directly affect the pressure or volume of the cylinder. However, it can indirectly affect it if the weight is pushing down on the piston and changing the pressure inside the cylinder. In this case, you would use the equation P = F/A, where F is the weight and A is the area of the piston. This would be relevant for calculating the change in pressure in the cylinder due to the weight.

Additionally, it would be helpful to see your calculations and units for all parts of the problem to ensure accuracy. Overall, your reasoning seems sound, but it is important to show your work and units to fully understand and verify your solution.