Work done by product gas in reversible adiabatic expansion

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Homework Help Overview

The discussion revolves around calculating the work done by a product gas during a reversible adiabatic expansion, specifically in the context of a combustion reaction involving ethanol. Participants are exploring the relationships between pressure, volume, and temperature in this thermodynamic process.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss using the equation for work done in terms of pressure and volume, and consider integrating from initial to final volumes. There are questions about the initial conditions, such as whether to assume a specific initial pressure. Some participants inquire about the parameters known for the gas before expansion, including initial volume, temperature, and the number of moles.

Discussion Status

The discussion is active, with participants providing insights and asking clarifying questions about the initial state of the gas and the relationships between the variables involved. There is a focus on deriving equations and understanding the implications of the ideal gas law in this context.

Contextual Notes

Participants note specific values such as the initial and final volumes, initial temperature, and the amount of reactants involved in the combustion reaction. There is an emphasis on understanding the initial conditions and their impact on calculations.

Egbert
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posted in general physics forum, please wait for OP to show work
I am having trouble calculating the work done by a product gas in reversible adiabatic expansion, and in calculating the final temperature. pV gamma = constant, Cv = constant (assume), gamma = cv + nR / Cv.
anyone who can help me out?
 
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Work done = ∫P.dV
PVγ = P1V1γ = P2V2γ

Try substituting one equation in the other and integrating from V1 to V2
 
I only know the V1, V2 and n. Should this work or should I assume a P1 of 1 bar?
 
What parameters do you know about the gas in its initial state before the expansion?

Chet
 
I
Chestermiller said:
What parameters do you know about the gas in its initial state before the expansion?

Chet
t is a combustion reaction of ethanol, volume is increasing from 0.02 m3 to 0.04 m3 with a starting temperature of 4000 K. Also the amounts are known. (12g ethane and enough oxygen)
Thanks
 
Egbert said:
I

t is a combustion reaction of ethanol, volume is increasing from 0.02 m3 to 0.04 m3 with a starting temperature of 4000 K. Also the amounts are known. (12g ethane and enough oxygen)
Thanks
You know the initial volume, the initial number of moles of gas, and the initial temperature. From the ideal gas law, what do you get for the initial pressure?

Chet
 
Using PV = nRT and PVγ = constant, can you devise an equation with 'V' and 'T'?
 

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