Work Done by Isothermal Expansion

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Homework Help Overview

The discussion revolves around the calculation of work done during the isothermal expansion of an ideal gas under various conditions, including expansion against a vacuum and against a constant external pressure. Participants are exploring the implications of the ideal gas law and the definitions of work in thermodynamic processes.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to calculate the volume of the gas using the ideal gas law and question how to approach the calculation of work when both pressure and volume change. They explore the differences in calculations for various scenarios of expansion.

Discussion Status

There is an ongoing exploration of the different cases of work done, with some participants providing insights into how to express pressure in reversible processes. Guidance has been offered regarding the calculation of work done against external forces and in free expansion scenarios, but no consensus has been reached on specific numerical values or final calculations.

Contextual Notes

Participants are navigating the constraints of the problem, including the lack of initial and final volume values and the implications of expanding against a vacuum versus a constant external pressure. There is a recognition of the need for clarity on how to express and calculate work in these different contexts.

Calu
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Homework Statement


A quantity of ideal gas (0.800mole) at a pressure of 10.0atm and 200K is allowed to
expand isothermally until it reaches a pressure of 1.00atm. Calculate the work done
if this expansion is carried out a) against a vacuum, b) against a constant external
pressure of 1.0atm and c) reversibly.

I'm not even sure where to start here. I've only calculated work done using dW = ∫ PdV. However, I'm not given an initial or final volume here, so I'm not sure how to proceed. Any hints?
 
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It is ideal gas. Given the amount of gas, the pressure and the temperature. What is the volume?
 
ehild said:
It is ideal gas. Given the amount of gas, the pressure and the temperature. What is the volume?
I see, I simply rearrange PV = nRT?

In which case, how does my calculation change between each of the above instances?
 
Calu said:
I see, I simply rearrange PV = nRT?

In which case, how does my calculation change between each of the above instances?
I do not see any calculations of yours. :)
 
ehild said:
I do not see any calculations of yours. :)

How would I go about calculating work when both the pressure and the volume change? I can integrate P.dV and put in the values for the initial and final volumes, but what value of pressure do I use?
 
Calu said:
How would I go about calculating work when both the pressure and the volume change? I can integrate P.dV and put in the values for the initial and final volumes, but what value of pressure do I use?
Pressure is only defined for reversible (quasi-static) process. In that case, you can express P from the ideal gas law.

In the other cases, you can calculate the work done on the gas by external forces.
What is the work done on the gas if there is no external force (when the gas expands into vacuum)?
What is the work done on the gas if the external pressure is constant (1.0 atm)?
 
ehild said:
Pressure is only defined for reversible (quasi-static) process. In that case, you can express P from the ideal gas law.

In the other cases, you can calculate the work done on the gas by external forces.
What is the work done on the gas if there is no external force (when the gas expands into vacuum)?
What is the work done on the gas if the external pressure is constant (1.0 atm)?

Okay, so in the reversible case I can substitute nRT ∫ 1/V .dV = nRT ln(V2-V1). I'm not sure how to work out the other two cases though.
 
What is the work done if no force is exerted?
What is the work done by the environment on the gas if the external pressure is 1.0 atm and the volume changes from V1 to V2?
 
ehild said:
What is the work done if no force is exerted?
What is the work done by the environment on the gas if the external pressure is 1.0 atm and the volume changes from V1 to V2?

Okay, so in the first case, I would say no work is being done on the gas, however the question just asks for the work done. Is the gas doing work on the surroundings in this case? In the second case I would say that the numerical value of work done is equivalent to the difference between the volumes.
 
  • #10
Calu said:
Okay, so in the first case, I would say no work is being done on the gas, however the question just asks for the work done. Is the gas doing work on the surroundings in this case?
Is there anything to do work on if the gas expands freely?
Calu said:
In the second case I would say that the numerical value of work done is equivalent to the difference between the volumes.
It is the constant external pressure multiplied by the difference of volumes, and the external pressure is 1.0 atm,
 
Last edited:
  • #11
ehild said:
Is there anything to do work on if the gas expands freely?

It is the constant external pressure multiplied by the difference of volumes, and the external pressure is 1.0 atm, so you are right...

In first case, I guess not. That makes sense. In the second case I apologise for omitting the multiplication by 1, its how I've been taught. I very really show multiplication by 1 in my working.
 
  • #12
Calu said:
In first case, I guess not. That makes sense. In the second case I apologise for omitting the multiplication by 1, its how I've been taught. I very really show multiplication by 1 in my working.
It is not multiplication by 1 but multiplication by 1.0 atm. And the result should be in joules. So what is the numerical value at the end?
 

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