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 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 63 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 32C, how hot does it get after being compressed? Answer in units of C.

Explanation / Answer

We know that,

For Ideal gas from Thermodynamics,

P1V1 / T1 = P2V2/ T2

So, T2 = T1 (P2V2 / P1V1) = 32(63*1/1*20) = 100.8 oC

So, due to compression from 32 oC to 100.8 oC is the change in temperature (i.e., additional of 68.8oC )

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