What equation would be used to estimate the temperature?

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    Estimate Temperature
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Discussion Overview

The discussion revolves around estimating the temperature of air in a Diesel engine after it is compressed to about 1/20 of its original volume. Participants explore the relevant equations and principles, including the adiabatic process and the ideal gas law, while also addressing the nature of the compression process.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks for help in estimating the temperature of air in a Diesel engine after compression and inquires about the role of spark plugs.
  • Another participant suggests using the adiabatic condition \left(PV^\gamma = \textit{constant}\right) to determine the pressure after compression and then applying the ideal gas law \left(PV = nRT\right) to find the temperature.
  • A participant questions the assumption of an adiabatic process, asking whether it is an approximation and expressing concern about heat transfer to the cylinder wall.
  • In response, a participant argues that the rapid nature of the compression implies insufficient time for significant heat transfer to occur, supporting the adiabatic assumption.
  • One participant expresses gratitude for the clarification regarding the adiabatic process, indicating that it makes sense to them.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the assumption of adiabatic conditions, as there is a question raised about the validity of this approximation. The discussion includes both support for and skepticism about the adiabatic model.

Contextual Notes

The discussion does not resolve the potential heat transfer to the cylinder wall or the implications of the rapid compression on the adiabatic assumption.

jlmac2001
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Can someone help me get started on this question?:

In a Diesel engine, atmospheric air is quickly compressed to about 1/20 of its original volume. Estimate the temperature of the air after compresion and explain why a Diesel engine does not require spark plugs.


What equation would be used to estimate the temperature?
 
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Use the adiabatic condition [itex]\left(PV^\gamma = \textit{constant}\right)[/itex] to find the pressure in the cylinder after the volume has been reduced to 1/20 of its initial volume.

Next, use the ideal gas law [itex]\left(PV = nRT\right)[/itex] to calculate the temperature.

- Warren
 
chroot, how do you know it's adiabatic? Is this an approximation? I don't see how heat is prevented from transfer to the cylinder wall.
 
The key word is "quickly." Given that the compression happens quickly, not enough time is available for significant heat transfer to occur.

- Warren
 
Thanks chroot. That's exactly the kind of clarification I was looking for, and it makes sense to me now.
 

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