Truck cylinder, ideal gas law problem

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SUMMARY

The discussion focuses on solving a thermodynamics problem involving a diesel engine cylinder with an initial volume of 500 cm³, where air is compressed from an initial state of 30°C and 1.0 atm pressure. The work done on the air is 450 J, leading to a calculated final temperature of 1100°C. The final volume was determined using the formula W = PVγ(Vf1-γ - Vi1-γ) / (1 - γ), which effectively resolves the issue of finding the final volume after compression.

PREREQUISITES
  • Understanding of the Ideal Gas Law (PV = nRT)
  • Familiarity with thermodynamic work equations
  • Knowledge of specific heat capacities and the concept of γ (gamma)
  • Basic principles of gas compression in engines
NEXT STEPS
  • Study the derivation and application of the Ideal Gas Law in real-world scenarios
  • Learn about the significance of specific heat ratios (γ) in thermodynamic processes
  • Explore advanced thermodynamic equations for work done during gas compression
  • Investigate the behavior of gases under varying pressure and temperature conditions
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, mechanical engineers working with internal combustion engines, and anyone interested in the principles of gas behavior under compression.

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Homework Statement



One cylinder in the diesel engine of a truck has an initial volume of 500 cm^3. Air is admitted to the cylinder at 30 C and a pressure of 1.0 atm. The piston rod then does 450 J of work to rapidly compress the air. What is its final temperature? What is its final volume?

Homework Equations



PV = nRT
\Delta Eth = (5/2)nR\DeltaT

The Attempt at a Solution



I found the temperature using the second equation to be 1100 C which is right. However i cannot find the final volume for the life of me. I tried P\gamma - 1T-\gamma and use the final pressure to find the volume but that didn't seem to work. Is there another way to go about this?
 
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finally figured it out using the formula:

W = PV\gamma(Vf1-\gamma - Vi1-\gamma)/(1 - \gamma)
 

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