Work done by product gas in reversible adiabatic expansion

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SUMMARY

The discussion focuses on calculating the work done by a product gas during reversible adiabatic expansion, specifically for a combustion reaction involving ethanol. Key equations mentioned include the relationship PVγ = constant and the ideal gas law PV = nRT. Participants discuss the initial parameters, including initial volume (0.02 m3 to 0.04 m3), initial temperature (4000 K), and the amount of gas (12g of ethane). The integration of work done is highlighted as ∫P.dV, emphasizing the need to determine initial pressure for accurate calculations.

PREREQUISITES
  • Understanding of the ideal gas law (PV = nRT)
  • Familiarity with adiabatic processes and the concept of γ (gamma)
  • Knowledge of integration techniques in thermodynamics
  • Basic principles of combustion reactions
NEXT STEPS
  • Study the derivation of work done in reversible adiabatic processes
  • Learn about the specific heat capacities (Cv and Cp) and their role in thermodynamic calculations
  • Explore the application of the ideal gas law in varying conditions
  • Investigate the effects of temperature and pressure changes on gas behavior during expansion
USEFUL FOR

Students and professionals in thermodynamics, chemical engineering, and physical chemistry who are involved in analyzing gas behavior during adiabatic processes and combustion reactions.

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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