Why are isothermal process values higher than adiabatic ones?

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Discussion Overview

The discussion revolves around the comparison of isothermal and adiabatic processes in thermodynamics, specifically focusing on why values associated with isothermal processes are higher than those for adiabatic processes. Participants explore the characteristics of each process, the implications of temperature maintenance, and the mathematical relationships involved.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants inquire about the defining qualities of isothermal processes and what is necessary to maintain them.
  • There is a discussion about the differences in expansion characteristics between isothermal and adiabatic processes, with some participants noting that the adiabatic curve is steeper than the isothermal curve.
  • Participants mention the role of temperature in isothermal processes and the need for heat exchange to maintain constant temperature.
  • Some participants propose that the adiabatic process can only exchange work, while the isothermal process can exchange both heat and work.
  • There is a request for a mathematical proof to demonstrate the steeper nature of the adiabatic curve compared to the isothermal curve, referencing the ideal gas equation of state.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the characteristics of isothermal and adiabatic processes, with some agreeing on the need for heat exchange in isothermal processes while others challenge or refine earlier claims. The discussion remains unresolved regarding the mathematical proof of the curve steepness.

Contextual Notes

Participants reference the concept of "gamma" in relation to adiabatic processes, but the implications of this and other assumptions are not fully explored or agreed upon. There are also unresolved questions about the specific mathematical relationships that differentiate the two processes.

Ana Mido
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why are isothermal process values higher than adiabatic process ones?
I know that the volume is powered by gama in adiabatic process ones, and this has an effect.
but how can I explain it ?!
http://www.popsolving.com/Thermodynamics/Problem2.4_Freebody.jpg
 
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Ana Mido said:
why is isothermal process values higher than adiabatic process ones?
What is the defining quality of an isothermal process? What do you need to maintain that quality?
 
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Bystander said:
What is the defining quality of an isothermal process? What do you need to maintain that quality?
I want to know why when I draw this relation, the isothermal is above & adiabatic is below. I know this is because of the power "gama"
Are there any other reasons ?
 
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You're looking at two expansions, an isothermal, and an adiabatic. What's going on in the isothermal expansion that is not going on in the adiabatic expansion?
 
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Bystander said:
You're looking at two expansions, an isothermal, and an adiabatic. What's going on in the isothermal expansion that is not going on in the adiabatic expansion?
ok, sorry I've put the question in wrong meaning.
 
Ana Mido said:
ok
That means you see the difference?
 
Bystander said:
That means you see the difference?
OK, I want to know why is the adiabatic curve steeper than the isothermal one?
 
What do you have to add to the isothermal process to keep it isothermal?
 
Bystander said:
What do you have to add to the isothermal process to keep it isothermal?
I have to make the temperature still constant.
 
  • #10
Ana Mido said:
I have to make the temperature still constant.
Yes. Excellent. And how do you do that?
 
  • #11
Bystander said:
Yes. Excellent. And how do you do that?
I don't know really.
but may be by closing the system or isolating it ? right ?
 
  • #12
Ana Mido said:
or isolating it ? right ?
Wrong. The adiabatic system is closed (no exchange of matter) and insulated, exchanging only work with its surroundings. The isothermal system is closed and not insulated, so it can exchange work and what else with its surroundings?
 
  • #13
Bystander said:
Wrong. The adiabatic system is closed (no exchange of matter) and insulated, exchanging only work with its surroundings. The isothermal system is closed and not insulated, so it can exchange work and what else with its surroundings?
The closed system exchange energy with surroundings & the mass is still constant
 
  • #14
Ana Mido said:
exchange energy
What kind of energy?
 
  • #15
Bystander said:
What kind of energy?
heat or work
 
  • #16
"Or?" Are you certain it's only one or the other?
 
  • #17
Bystander said:
"Or?" Are you certain it's only one or the other?
no, the both
 
  • #18
Okay. Now, compare this to the adiabatic process that can only exchange work with the surroundings.
 
  • #19
Bystander said:
Okay. Now, compare this to the adiabatic process that can only exchange work with the surroundings.
That's right !
In isothermal: Q=W & T is constant , exchange both
In Adiabatic: Q=0 & W=-ΔU , exchange only work
Is that right ?!
 
  • #20
Close enough. The isothermal process picks up extra heat from some external reservoir that maintains the temperature of the working fluid, and that can be converted to work.
 
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  • #21
You're right !
Then, how can I prove that Adiabatic curve is more steeper than isothermal curve , using mathematics ?
 
  • #22
You're looking at dP/dT for the two processes, and you want to show that it is more negative for the adiabatic process. From the original problem statement, it appears you can use the ideal gas equation of state. You know that T is constant for the isothermal process, and that T is a function of P, and V for the adiabatic process.
 

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