- #1
TonyG
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original post was cut off half way through, so I'm re-posting:
What I'm really trying to understand has to do with superchargers, and a phenomenon I (and others) observe at the track every season: more boost in colder weather.
The common explanation for this is that air is denser in the cold weather, resulting in more boost. Another variation is that the (adiabatic) compressibility is higher for the colder air, which sort of reduces to the same argument.
Now my thermo is a little rusty, but if it's that simple, then I would expect that this effect can be shown with a simple adiabatic compression model on an ideal gas (approximating air as an ideal gas). Is there a simple expression showing that if you do some amount of work W adiabatically (lets say a piston/cylinder configuration) that the final P reached will be higher when the initial air temperature is lower (or initial air density is higher, assuming density is proportional to P/T)?
I can't find such an expression in any of my thermo books. And when I try to derive an expression, both initial density and initial temperature eventually cancel out of the equation, and P_final becomes only a function of W and the specific heat. Since the process is adiabatic, I've been using [tex]PV^{\gamma} [/tex] = constant and taking dT = W/Mc (M = density * volume, c = specific heat, ignoring temperature dependence of c).
Another explanation is that the above effect isn't a "density thing", but rather a result of better efficiency in the colder weather.
I'm hardly an expert on compressor physics. If anyone can shed some light on this, I'd really appreciate it. Sorry for the long post.
What I'm really trying to understand has to do with superchargers, and a phenomenon I (and others) observe at the track every season: more boost in colder weather.
The common explanation for this is that air is denser in the cold weather, resulting in more boost. Another variation is that the (adiabatic) compressibility is higher for the colder air, which sort of reduces to the same argument.
Now my thermo is a little rusty, but if it's that simple, then I would expect that this effect can be shown with a simple adiabatic compression model on an ideal gas (approximating air as an ideal gas). Is there a simple expression showing that if you do some amount of work W adiabatically (lets say a piston/cylinder configuration) that the final P reached will be higher when the initial air temperature is lower (or initial air density is higher, assuming density is proportional to P/T)?
I can't find such an expression in any of my thermo books. And when I try to derive an expression, both initial density and initial temperature eventually cancel out of the equation, and P_final becomes only a function of W and the specific heat. Since the process is adiabatic, I've been using [tex]PV^{\gamma} [/tex] = constant and taking dT = W/Mc (M = density * volume, c = specific heat, ignoring temperature dependence of c).
Another explanation is that the above effect isn't a "density thing", but rather a result of better efficiency in the colder weather.
I'm hardly an expert on compressor physics. If anyone can shed some light on this, I'd really appreciate it. Sorry for the long post.
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