Double Pressure: What are the Effects on Temperature & Volume?

[JerLynn]

Homework Statement

say you have a thermally insulated box which is separated into equal parts by a thermally insulated piston (frictionless) and each part has the same number of molecules and both sides are both at the same initial temperature, pressure, and volume and have the same constant heat capacity at constant volume (Cv=5/2Nk)

assume somehow you can slowly heat one side until its pressure doubles, what is the effect on each side's temperature and volume?

Homework Equations

PV=nRT, PV=NkT

The Attempt at a Solution

if pressure goes up then volume can go down or temperature can increase or some combination of the two, so the heated side should either get smaller or get warmer if the pressure doubles. but there isn't anything that would do compression work on the heated side, so it doesn't seem like it should get smaller.

how you can know how each of the variables changes independently of each other on either side. seems like the heated side could increase in pressure by increasing in temperature at constant volume or by increasing in volume a bit and increasing in temperature even more. same for the other side

is there a way to know how temp/volume on each side change independtly of each other or can you only deal with ratios of the variables

thx

 

[mgb_phys]

Since the piston is frictionless you have to assume it will move to give the same pressure on each side of the box.
Since no gas can pass between the sides 'n' is constant on both sides so PV/T is a constant.
The pressure on both sides is the same and the total volume is constant so you know.

P1V1/T1 = P2V2/T2
but P1=P2 and V1+V2=constant=V

 

[JerLynn]

thx for the response

is there any way to separate out the changes in temperature and volume on each side instead of just saying that PV/T is constant? like saying the volume changed by this much and the temperature by this much in expressions separate from each other knowing just the initial temp, volume, pressure and the change in pressure and the heat capacity

im doing online assignments and it wants me to type in the changes in temp/volume in terms of the initial state, and wants the temp change as an answer separate from the volume change. i don't know how to separate out the temp and volume just from what is given. maybe something to do with the heat capacity? i am very confused about what is being overlooked by me

 

[mgb_phys]

Not really - you could for instance ,double the tempearature on both sides without changing the volume or pressure.
You do have the extra constraints that the total volume is constant and the pressures are equal.

 

[JerLynn]

there is a way of doing it according to my teacher by considering the process on the left and how P and V are related, according to her

im just lost, i don't even know what kind of process this is. the volume isn't constant, the temp isn't constant, the pressure isn't constant...all i know is one side is being heated and its pressure grows. there must be something fundamental i am not seeing

 

[mgb_phys]

They are related by the extra constraints.
1, The total volume is constant =V1+V2
2, The pressures on each side are the same.