Temperature & Pressure. Beginner Physics.

Click For Summary
SUMMARY

The discussion focuses on a physics problem involving a rigid, insulated container divided by a membrane, initially containing gas at absolute temperature To and pressure Po. When a hole forms in the membrane, the gas expands to occupy double its original volume. Using the Ideal Gas Law (PV=nRT), it is established that the new pressure (P2) and temperature (T2) of the gas will result in the relationship P2/T2 = 0.5 * (Po/To), indicating that both pressure and temperature are halved after the gas expands.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV=nRT)
  • Basic knowledge of thermodynamics and gas behavior
  • Familiarity with concepts of pressure and temperature in physics
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the implications of gas expansion in thermodynamic systems
  • Learn about the concepts of adiabatic and isothermal processes
  • Explore real-world applications of the Ideal Gas Law
  • Investigate the effects of changing volume on gas properties
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding gas behavior under changing conditions, particularly in thermodynamics and ideal gas scenarios.

Nachore
Messages
16
Reaction score
0

Homework Statement


A rigid, perfectly insulated container has a membrane dividing its volume in half. One side contains a gas at an absolute temperature To and pressure Po, while the other half is completely empty. Suddenly a small hole develops in the membrane, allowing the gas to leak out into the other half until it eventually occupies twice its original volume. In terms of To and Po, what will be the new temperature and pressure of the gas when it is distributed equally in both halves of the container?

Homework Equations


None.


The Attempt at a Solution


I have no idea how to explain this answer. I don't know how to approach this. Please help.
 
Physics news on Phys.org
The box has a definite volume of V and a definite amount of mass inside (n). If the gas starts off with a volume of V, Pressure of Po, Temp of To, and mass of n, use the Ideal Gas Law to solve for a change in volume and respective pressure/temperature changes.

PV=nRT where R is the ideal gas constant.

Case 1, Po*V=n*R*To
Case 2 P2*V2=n*R*T2

Po/To=(nR)/V
P2/T2=nR/V2

Since V2=2*V then P2/T2=0.5(nR)/V or the ratio of the pressure to the temperature of the final volume of gas will be half that of the original. P2/T2=.5*Po/To
 

Similar threads

Gas temperature in a constant volume
  • · Replies 8 ·
Replies
8
Views
2K
Adiabatic Expansion of Pressurized Air in a Piston-Cylinder Setup
  • · Replies 8 ·
Replies
8
Views
2K
Thermally insulated container with alternating series of walls
  • · Replies 49 ·
2
Replies
49
Views
4K
Internal energy of an ideal gas as a function of temperature
  • · Replies 2 ·
Replies
2
Views
4K
Mixing two gases in an isolated system and calculating final p and T
  • · Replies 4 ·
Replies
4
Views
3K
Thermal energy problem: Gas expansion in cylinder
  • · Replies 3 ·
Replies
3
Views
3K
Pressure/Temperature mechanical equilibrium
  • · Replies 6 ·
Replies
6
Views
3K
Pressurized gas container gets opened
  • · Replies 1 ·
Replies
1
Views
2K
Final Temperature of Ideal Gas in Constant Pressure and Volume Compression
  • · Replies 2 ·
Replies
2
Views
5K
Pressure-Volume Work
  • · Replies 7 ·
Replies
7
Views
1K