Why are isothermal process values higher than adiabatic ones?

In summary: So, you can use P, V, and T to solve for dP/dT. But how do you know that the dP/dT for the adiabatic process is more negative than the dP/dT for the isothermal process?That's right !
  • #1
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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  • #2
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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  • #3
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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  • #4
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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  • #5
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.
 
  • #6
Ana Mido said:
ok
That means you see the difference?
 
  • #7
Bystander said:
That means you see the difference?
OK, I want to know why is the adiabatic curve steeper than the isothermal one?
 
  • #8
What do you have to add to the isothermal process to keep it isothermal?
 
  • #9
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.
 

1. Why is the temperature higher in an isothermal process compared to an adiabatic process?

In an isothermal process, the temperature remains constant throughout the process. This means that any heat added or removed is immediately balanced by an equal amount of heat lost or gained, resulting in no net change in temperature. In contrast, in an adiabatic process, no heat is allowed to enter or leave the system, so any change in temperature must be due to work being done. This means that the temperature change in an adiabatic process is typically lower than in an isothermal process.

2. How does the heat transfer differ between an isothermal and adiabatic process?

In an isothermal process, the heat transfer is equal to the work done, meaning that the temperature remains constant. In an adiabatic process, no heat is allowed to enter or leave the system, so all work done results in a change in temperature. This means that the heat transfer is typically lower in an adiabatic process compared to an isothermal process.

3. Why do isothermal processes have higher entropy changes than adiabatic processes?

Entropy is a measure of the disorder or randomness of a system. In an isothermal process, the temperature remains constant, so the system's energy is evenly distributed, resulting in a higher degree of disorder. In an adiabatic process, the temperature change is lower, leading to a lower degree of disorder and a lower entropy change.

4. How does the work done vary between an isothermal and adiabatic process?

In an isothermal process, the work done is equal to the heat transfer, as the temperature remains constant. In an adiabatic process, no heat is allowed to enter or leave the system, so all work done results in a change in temperature. This means that the work done is typically higher in an isothermal process compared to an adiabatic process.

5. Why is the pressure change greater in an adiabatic process compared to an isothermal process?

In an adiabatic process, no heat is allowed to enter or leave the system, so all work done results in a change in temperature. This change in temperature leads to a greater change in pressure, as pressure and temperature are directly proportional according to the ideal gas law. In contrast, in an isothermal process, the temperature remains constant, resulting in a smaller change in pressure.

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