Isothermal compression vs thermally isolated compression

In summary: I struggled with this one for a little while and was about to go to my teacher for help when I found this on the internet. In summary, the homework statement is trying to say that the internal energy of the gas is the same no matter which way it is compressed, which is not true.
  • #1
balibone
3
0
1. Homework Statement
Two equal masses of an ideal gas initially at the same temperature and pressure are compressed to half of their initial volumes, one of them isothermally, and the other while thermally isolated from its surroundings.
Which one of the following is the same for both samples of the gas?
A) the heat given during compression
B) the internal energy of the compressed gas
C) the density of the compressed gas
D) the work done on the gas during compression
2. Relevant equations
Nil
3. The attempt at a solution
My initial thought was "is there a diff between 'isothermally' and 'thermally isolated from surroundings' ?". Or is it just a trick statement? i gave it a try and chose B as the answer cause i thought internal energy of ideal gas depends on its temperature. Since both are (i assumed) isothermally compressed, internal energy at the end must be the same, regardless of change in pressure or volume. Alas, my physics teacher posted answers on the net and it came out as C. WHY?
 
Physics news on Phys.org
  • #2
balibone said:
My initial thought was "is there a diff between 'isothermally' and 'thermally isolated from surroundings' ?". Or is it just a trick statement? i gave it a try and chose B as the answer cause i thought internal energy of ideal gas depends on its temperature. Since both are (i assumed) isothermally compressed, internal energy at the end must be the same, regardless of change in pressure or volume. Alas, my physics teacher posted answers on the net and it came out as C. WHY?
Thermally isolated from surroundings = adiabatic: no heat flow into or out of the gas.

In an adiabatic compression, dQ = 0 so dU = -dW where dW is the incremental work done BY the gas. Since work is done ON the gas to compress it, dU>0, so its temperature will increase. So adiabatic compression cannot be isothermal.

Heat must flow out of the gas to keep temperature constant in an isothermal compression. Heat cannot flow out in an adiabatic compression. Internal energy increases in the adiabatic compression but is constant in the isothermal compression.

So A and B are out. Since the work done on the gas depends on the pressure of the gas which is proportional to the temperature at a given volume, the adiabatic compression requires more work at the gas heats up. So D is out. That leaves C. Since [itex]\rho = n/V[/itex], density does not depend on how the gas is compressed.

AM
 
  • #3
thanks a lot man!
 

1. What is the difference between isothermal compression and thermally isolated compression?

Isothermal compression is a process where the temperature of a system remains constant during compression, while thermally isolated compression is a process where the system is not allowed to exchange heat with its surroundings during compression.

2. Which process is more efficient in compressing gases?

Isothermal compression is more efficient in compressing gases because it requires less work and results in a smaller change in temperature compared to thermally isolated compression.

3. What are the advantages of isothermal compression?

The advantages of isothermal compression include lower energy consumption, reduced wear and tear on equipment, and the ability to compress gases to higher pressures without significant temperature increases.

4. Why is thermally isolated compression used in some cases?

Thermally isolated compression is used in cases where the change in temperature during compression can have a significant impact on the properties of the gas, such as in chemical reactions or sensitive experiments.

5. Can isothermal compression and thermally isolated compression be used interchangeably?

No, isothermal compression and thermally isolated compression are two distinct processes with different outcomes. They cannot be used interchangeably as they have different effects on the temperature and properties of the gas being compressed.

Similar threads

  • Introductory Physics Homework Help
Replies
17
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
33
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
3K
  • Thermodynamics
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
923
  • Introductory Physics Homework Help
2
Replies
60
Views
5K
  • Thermodynamics
Replies
20
Views
1K
Back
Top