Compressing gases requires work and the resulting energy is usually converted to

Question

Compressing gases requires work and the resulting energy is usually converted to heat; if this heat does not escape, the gas’s temperature 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 60 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 13C, how hot does it get after being compressed? Answer in units of C.

Explanation / Answer

1V = nR(273+13)

60*V/20 = nR T

1/3 = (286/T)

T= 286*3 =858 K

=858-273 =585 C

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