What is the final volume of container B?

Click For Summary

Homework Help Overview

The discussion revolves around a thermodynamics problem involving two containers of gas, one rigid and one with a movable piston. The scenario includes heating both containers with identical heaters and seeks to determine the final volume of the container with the piston after a specified time and power input.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the initial pressures and the use of the ideal gas law to find the number of moles of gas. They explore energy calculations based on the power of the heaters and the time they are applied. Some express confusion about the relevance of the rigid container A and question the assumptions made regarding energy distribution between the two containers.

Discussion Status

There is ongoing exploration of the problem with various approaches being discussed. Some participants have offered hints regarding energy calculations and the relationship between work and pressure, while others are questioning their understanding of the equations and the assumptions involved.

Contextual Notes

Participants note that the problem involves a rigid container and a container with a piston, which may affect how energy is shared and work is done. There is uncertainty about the correct equations to use, particularly regarding constant pressure and the implications of the piston's movement.

skinard360
Messages
18
Reaction score
0
Two 800\; cm^3 containers hold identical amounts of a monatomic gas at 20^\circ C. Container A is rigid. Container B has a 100\; cm^2 piston with a mass of 10 kg that can slide up and down vertically without friction. Both containers are placed on identical heaters and heated for equal amounts of time.
Suppose the heaters have 25 W of power and are turned on for 15 s. What is the final volume of container B?


I found the initial pressures of both container B, I then plugged that into the initial pV=nRT to find n, then plugged that into
E=[nc(constant pressure)deltaT] using 25x15=375 J as the value for E. This determined delta T, I then plugged that (with T = delta T + 293) into the final pV=nRT to get V. This seems like it's probably too complicated, and I didn't get the right answer...can someone please help??
 
Physics news on Phys.org
skinard360 said:
Two 800\; cm^3 containers hold identical amounts of a monatomic gas at 20^\circ C. Container A is rigid. Container B has a 100\; cm^2 piston with a mass of 10 kg that can slide up and down vertically without friction. Both containers are placed on identical heaters and heated for equal amounts of time.
Suppose the heaters have 25 W of power and are turned on for 15 s. What is the final volume of container B?


I found the initial pressures of both container B, I then plugged that into the initial pV=nRT to find n, then plugged that into
E=[nc(constant pressure)deltaT] using 25x15=375 J as the value for E. This determined delta T, I then plugged that (with T = delta T + 293) into the final pV=nRT to get V. This seems like it's probably too complicated, and I didn't get the right answer...can someone please help??

I'm somewhat confused with your notation 100\; and I don't know what the significance of container A is.
 
that should just be 100 cm squared. I'm not sure what the significance is of container A is either...it may have to do with question (a) which asked which container would have the higher final temp. Do you think container A should have some part in the answer?
 
skinard360 said:
that should just be 100 cm squared. I'm not sure what the significance is of container A is either...it may have to do with question (a) which asked which container would have the higher final temp. Do you think container A should have some part in the answer?

ahh, ok, A seems to be only for part a).

I'll poke at b) and give you hints

to start you off, they give you power (in watts) and the length of time that power is exposed to the system. Power has energy of units over time and time has units of time. Using those two quantities, you should be able to calculate the energy put into the system by the heaters.

furthermore, Boltzmann's constant and temperature are equatable to energy.
 
Last edited:
I think... that container A and B share the energy from the heater.
 
that would be the thermal energy, right? 375 J...did I use the right equation above with E=ncdeltaT with c=20.8 ? or should it be another equation, since that equation is assuming that the pressure in the system stays constant
 
Also, for constant pressure, W = P(del V)

(work equals pressure times the change in volume)

which can be represented as W = P(V2 - V1)
 
skinard360 said:
that would be the thermal energy, right? 375 J...did I use the right equation above with E=ncdeltaT with c=20.8 ? or should it be another equation, since that equation is assuming that the pressure in the system stays constant

What is c? That looks an awful lot like part of the phase change equation which shouldn't be used here, that's for when a material changes form (from liquid to gas and such)
 
I tried another equation to get the final temp...thermal energy = 375 = (3/2)NkBT...then plugged it into pv=nRT but this didn't work either
For the work equation above, does work = 375? I feel like I'm getting more confused the further I go
 
  • #10
I'm not quite sure about this. Let me play with it more and get back to it
 
  • #11
Kenny Lee said:
I think... that container A and B share the energy from the heater.

This may be a good point too, I'm not sure. What's the answer so I know when I get it?
 
  • #12
I'm not sure what the answer is...sorry
 
  • #13
but I know the initial pressure is 1.097 atm
 
  • #14
note that in B, some of the work is going to go into lifting the piston:

W=mgh
 
  • #15
skinard360 said:
but I know the initial pressure is 1.097 atm

then why wouldn't W = P(V2-V1) work then? pressure stays constant if volume is allowed to change (i.e. the piston)

You just have to make sure you use the right W (that is, whether it's the full energy delivered by the heaters or only half.
 
  • #16
skinard360 said:
Two 800\; cm^3 containers hold identical amounts of a monatomic gas at 20^\circ C. Container A is rigid. Container B has a 100\; cm^2 piston with a mass of 10 kg that can slide up and down vertically without friction. Both containers are placed on identical heaters and heated for equal amounts of time.
Suppose the heaters have 25 W of power and are turned on for 15 s. What is the final volume of container B?I found the initial pressures of both container B, I then plugged that into the initial pV=nRT to find n, then plugged that into
E=[nc(constant pressure)deltaT] using 25x15=375 J as the value for E. This determined delta T, I then plugged that (with T = delta T + 293) into the final pV=nRT to get V. This seems like it's probably too complicated, and I didn't get the right answer...can someone please help??

How did you determine the pressure in A and/or the volume in B?

AM
 

Similar threads

Work done on container receiving gas from high pressure container
  • · Replies 1 ·
Replies
1
Views
2K
Thermally insulated container with alternating series of walls
  • · Replies 49 ·
2
Replies
49
Views
4K
Internal energy of a container filled with water & steam
  • · Replies 12 ·
Replies
12
Views
2K
Compute the Work: Pressure analogous to Volume
  • · Replies 4 ·
Replies
4
Views
1K
Gas in mercury manometer, finding its normal volume
  • · Replies 2 ·
Replies
2
Views
2K
Pressure of a fluid contained in a steel container
  • · Replies 7 ·
Replies
7
Views
2K
Volume ratio in an adiabatic gas expansion
  • · Replies 9 ·
Replies
9
Views
2K
I try to solve a thermodynamics problem on heat transfer
  • · Replies 3 ·
Replies
3
Views
2K
What is the final volume of the container?
  • · Replies 5 ·
Replies
5
Views
2K
What is the Ideal Gas Force on a Container at Temperature T?
  • · Replies 16 ·
Replies
16
Views
6K