Essentially comparison of isothermal and adiabatic transformations

In the isothermal transformation, PV is constant, so P1V1 = P2V2. In the adiabatic transformation, PV<sup>γ</sup> is constant, so P1V1<sup>γ</sup> = P3V2<sup>γ</sup>. You should be able to answer the question easily from these equations.In summary, two identical samples of ideal gas undergo different transformations, one isothermal and one adiabatic. Using the ideal gas law and the first and second laws of thermodynamics, we can determine that if P3<P2, then V2>V1. This is due to the equations P1V1 = P2V2 and
  • #1
arhont
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Homework Statement




Two identical samples of ideal gas are initially at P1 and V1. The first sample undergoes an isothermal transformation to P2, V2 and second sample undergoes an adiabatic transformation to P3, V2. If P3<P2, is V2 higher or lower than V1? Explain



Homework Equations



Ideal Gas Law, Thermo Laws.

The Attempt at a Solution



P1V1 --isotherm-->P2V2
P1V1 --adiabatic-->P3V2
If P2>P3, is V2>V1 or V2<V1?
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For isotherm we have ΔU=Q+W, but since there is ΔT=0, then via 1st law of Thermo - ΔU=0 and Q=-W.
For adiabatic we have constant heat, Q=0, W=PΔV, ΔU=W=PΔV. Yet... it seems useless. My gut tells me V2>V1, though somehow I am having trouble wrapping my mind around it.
 
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  • #2
There are two very useful equations relating pressure and volume, one for isothermal and one for adiabatic. You've met these, I would think.
 

Related to Essentially comparison of isothermal and adiabatic transformations

1. What is the difference between isothermal and adiabatic transformations?

Isothermal transformations occur at a constant temperature, while adiabatic transformations occur without heat exchange with the surroundings.

2. How do the pressure and volume change during an isothermal transformation?

In an isothermal transformation, the pressure and volume are inversely proportional, meaning that as one increases, the other decreases.

3. What is the relationship between temperature and internal energy in an adiabatic transformation?

In an adiabatic transformation, there is no heat exchange, so the internal energy remains constant while the temperature changes.

4. How do isothermal and adiabatic processes affect the work done by a system?

In an isothermal process, the work done is equal to the change in internal energy, while in an adiabatic process, the work done is equal to the change in temperature.

5. Which type of transformation is more efficient for work production?

An adiabatic process is more efficient for work production as it does not involve any heat loss to the surroundings.

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