Gases & Pressure: Solving Homework Equations

[parwana]

Homework Statement

An expandable cylinder has its top connected to a spring with force constant 2.00 103 N/m. (See Fig. P10.58.) The cylinder is filled with 4.00 L of gas with the spring relaxed at a pressure of 1.00 atm and a temperature of 20.0°C.

(a) If the lid has a cross-sectional area of 0.0100 m2 and negligible mass, how high will the lid rise when the temperature is raised to T = 230°C?


(b) What is the pressure of the gas at 230°C?

Homework Equations

PV=nRT
PiVi/Ti= PfVf/Tf

The Attempt at a Solution

Ok I did Pf= Pinitial+ k(spring constant)(h)/Area
Also Vf= Vi + h(Area)

Then I plugged these into the PiVi/Ti= PfVf/Tf
and its not the right answer

What am I doing wrong?

 

[berkeman]

Looks reasonable at first glance. Can you show your math with units so we can check?

 

[parwana]

((1.013X10^5 Pascals)(.004m^3))/20 Celsius= (((1.013X10^5 Pascals + 2X10^3N/m X height)/0.0100 meters^2)(.004m^3 + 0.0100meters^2 X height))/all over 230 Celsius

 

[berkeman]

I guess I was looking for a more step-by step development, but whatever. Where is the 1atm of initial pressure again? What units are you using? Be sure to include *all* units to be sure that they are consistent.

 

[parwana]

the 1 atm of pressure= 1.013X10^5 Pascals

I edited it to include the units

 

[berkeman]

Are Pascals, ml, N and m all compatible units? What are the base units of Pascals? (Sorry, I don't know offhand)

It looks like in the first part of the righthand side, you are mixing units of Pascals = N? How can a pressure equal a force? Do you see what I mean about carrying your units along to help you check your equations and manipulations? And near the end there, it looks like you are saying that a ml = m^3?

 

[parwana]

1 Pa ≡ 1 N/m²

let me convert the ml to m^3, maybe that's the problem

 

[berkeman]

Remember, in order to add terms, they have to have the same base units. And the left and right hand sides of an equation must have the same base units...

 

[parwana]

I am doing something wrong, I am not getting it right

 

[berkeman]

Re-write the equation, being careful to keep your units consistent as I mentioned in post #8. I have to go now. Good luck.

 

[parwana]

I don't know what's wrong, its not getting the right answer

 

[parwana]

can someone help me and try it and see what I am doing wrong and the answer they get?

 

[Gokul43201]

Units for temperature?

 

[parwana]

^ I have it there in Celsius

 

[berkeman]

can someone help me and try it and see what I am doing wrong and the answer they get?

Show us the current version of your equation, with the corrected and checked units, and we'll try to help you. We don't do your work for you.

 

[parwana]

^ I have it written on top but if u want it again

((1.013X10^5 Pascals)(.004m^3))/20 Celsius= (((1.013X10^5 Pascals + 2X10^3N/m X height)/0.0100 meters^2)(.004m^3 + 0.0100meters^2 X height))/all over 230 Celsius

 

[berkeman]

But the units still look wrong to me, which implies that the equation is not formed correctly.

lefthand side --> [ Nm^2/C ]

righthand side --> [ ( ((N/m + N)/m) m^3 )/C ]

 

[parwana]

hmm I really don't know what I am doing wrong, this is so frustrating

 

[berkeman]

hmm I really don't know what I am doing wrong, this is so frustrating

I think the problem is that you are trying to do too much in one line, and are not being careful about the algebra and units. Try it this way:

What is the answer for PiVi/Ti= ? (show the units of the answer)

Then set that equal to PfVf/Tf (being careful about the algebra and units) and solve for h.

 

[Gokul43201]

Units for temperature?

^ I have it there in Celsius

I wasn't asking a question; I was giving you a hint!

Is Celcius the correct unit to describe thermodynamic temperature?