Compressing gases requires work and the re- sulting energy is usually converted

Question

Compressing gases requires work and the re-
sulting energy is usually converted to heat; if
this heat does not escape, the gas’s temper-
ature will rise. This effect is used in diesel
engines: The compressed air gets so hot that
when the fuel is injected, it ignites without
any spark plugs.
As an example, consider a cylinder in a
diesel engine in which air is compressed to
one twentieth of its original volume while the
pressure rises from 1 atm to 44 atm (absolute,
not gauge). Note that because the air heats
up while being compressed, its pressure rises
more than twenty-fold.
If the air is taken into the cylinder at 40C,
how hot does it get after being compressed?
Answer in units of C

Explanation / Answer

P1V1/P2V2 = T1/T2

1 x V/(44 x (V/12)) = (40 + 273)/(T2)

T2 = 1159.26 K

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