What equation would be used to estimate the temperature?

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In a Diesel engine, atmospheric air is compressed to about 1/20 of its original volume, resulting in a significant increase in temperature due to the adiabatic compression process. The relevant equations for this calculation include the adiabatic condition (PV^γ = constant) to determine pressure and the ideal gas law (PV = nRT) to find temperature. The discussion highlights that the rapid compression minimizes heat transfer to the cylinder walls, justifying the assumption of an adiabatic process. Diesel engines do not require spark plugs because the high temperature generated from compression ignites the fuel. Understanding these principles is crucial for estimating the temperature and explaining the ignition process in Diesel engines.
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 \left(PV^\gamma = \textit{constant}\right) 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 \left(PV = nRT\right) 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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