Thermodynamics - Adiabiatc Expansion

In summary: I'm sorry for the confusion. I meant to say that the final volume can be found by rearranging the equation V(initial) x T(initial)^(3/2) = V(final) x T(final)^(3/2) and solving for V(final). The final temperature cannot be found without knowing the heat capacity of the gas. In summary, the final volume of the gas can be found by rearranging the equation V(initial) x T(initial)^(3/2) = V(final) x T(final)^(3/2) and solving for V(final). However, the final temperature cannot be determined without knowing the heat capacity of the gas.
  • #1
kineticwave
3
0

Homework Statement



2.5 mol of an ideal gas which starts at 2.2 atm and 50 degrees Celsius does 2.4 kJ of work during an adiabatic expansion. What is the final volume of the gas? Express the result in the unit [m3].

Homework Equations



V(initial) x T(initial)^(3/2) = V(final) x T(final)^(3/2)

The Attempt at a Solution



I found the initial volume first using pV=nRT which I got to be 30.15L. But I'm not sure how to get the final temperature, nor the final volume for that matter.
 
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  • #2
What's the internal energy of the gas? How does a change in that relate to work done?
 
  • #3
What I've posted is literally all the information I was given when asked to complete the question... my professor is known for his incomprehensible and ambiguous questions.
 
  • #4
kineticwave said:
What I've posted is literally all the information I was given when asked to complete the question... my professor is known for his incomprehensible and ambiguous questions.
It is not possible to answer this question without knowing the heat capacity of the gas. You appear to be using 1/(γ-1)=3/2 which would make Cv = 3/2 and γ = 5/3

Are you told that this is a monatomic gas?

AM
 
Last edited:
  • #5
The question posted is all that I'm given. This professor is known for questions like these. It's a course called Biophysics.
 
  • #6
kineticwave said:
The question posted is all that I'm given. This professor is known for questions like these. It's a course called Biophysics.
So how do you know that 1/(γ-1) = 3/2? (you have put this in your equation). Only a monatomic gas would have Cv=3R/2; γ=5/3.

AM
 
  • #7
Just a thought
ΔU=nR∫(T/V)dV
where T can be represent by V
(VixTi)^3/2)=(VxT)^3/2=constant <-- calculate by sub initial conditions.
 
  • #8
henry407 said:
Just a thought
ΔU=nR∫(T/V)dV
Ok except for a - sign. If Q = 0 then ΔU = -∫PdV
where T can be represent by V
??How do you do that?

AM
 
  • #9
Re AM:
(VixTi)^3/2=(VxT)^3/2=constant
isn't it, since the whole process is Adiabiatic Expansion, the above equation satisfy in any time during the process.
 
  • #10
henry407 said:
Re AM:
(VixTi)^3/2=(VxT)^3/2=constant
isn't it, since the whole process is Adiabiatic Expansion, the above equation satisfy in any time during the process.
Ok. I see what you mean. That will work.

AM
 

1. What is adiabatic expansion in thermodynamics?

Adiabatic expansion is a process in thermodynamics where a gas expands without gaining or losing heat to its surroundings. This means that the internal energy of the gas remains the same during the expansion.

2. How is adiabatic expansion different from isothermal expansion?

In adiabatic expansion, there is no transfer of heat between the system and its surroundings, while in isothermal expansion, the temperature of the gas remains constant throughout the process. This means that in adiabatic expansion, the internal energy of the gas changes, while in isothermal expansion, the internal energy remains constant.

3. What is the relationship between pressure and volume in adiabatic expansion?

In adiabatic expansion, the relationship between pressure and volume is described by the adiabatic equation: P1V1^γ = P2V2^γ, where P1 and V1 are the initial pressure and volume of the gas, P2 and V2 are the final pressure and volume, and γ is the heat capacity ratio of the gas.

4. How does adiabatic expansion affect the temperature of a gas?

During adiabatic expansion, the temperature of a gas decreases. This is because the internal energy of the gas decreases as it expands without gaining heat from its surroundings. This decrease in temperature is greater than in isothermal expansion, where the temperature remains constant.

5. What are some real-life examples of adiabatic expansion?

One example of adiabatic expansion is the expansion of air in a bicycle pump. As the air is compressed and forced out of the pump, it expands adiabatically and its temperature decreases, resulting in the cooling of the pump. Another example is the expansion of air in a car engine during the combustion process, where the expansion is adiabatic and results in the production of mechanical work.

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