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 54 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 18C, how hot does it get after being compressed? Answer in units of C.

Explanation / Answer

P1V1/T1 = P2V2/T2

(1 atm)(1 V)/(18+273.15K) = (54 atm)(1/20 V)/T

1/(291.15K)=(54/20) / T

1/(291.15)=(2.7) / T

T = (291.15)(2.7)

T = 786.105 K

T - 273.15 = T in degrees C

786.105 - 273.15K = 512.955 degrees C

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