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The compression of air in a jet turbine is often approximated as an adiabatic process.

The governing equation is pv^(gamma) is constant in an adiabatic process. Gamma is the ratio Cp/Cv, where Cp is the specific heat for a constant pressure process and Cv is the specific heat for a constant volume process. Combining this with the ideal gas law you can derive the temperature-pressure relationship

T2/T1 = (p2/p1)^(kappa)

where kappa = (gamma-1)/gamma.

Keep in mind that everything has to be in absolute units (e.g. temperature in kelvins and pressure in Pa,absolute.)

For a diatomic gas, gamma=1.4, so kappa=0.286.

Therefore, the final temperature is

T2=T1*(p2/p1)^(kappa)

=213 K * (1000/250)^0.286

= 213 * 1.48658

= 316.6 K.

This is the ideal case. For engineering calculations a lower value of gamma is sometimes used (say 1.3).

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16y ago
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1mo ago

Assuming the air is compressed isentropically, the temperature of the air would increase as it is compressed. Using the ideal gas law, we can calculate the new temperature to be approximately -32°C inside the jet airliner.

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Q: What would the air temperature inside a conventional jet airliner be if outside air at an altitude of 10 km pressure of 250 mb and a temperature of -60C is brought inside and compressed to a 1000?
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