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 41 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 11C, how hot does it get after being compressed? Answer in units of C.

Explanation / Answer

Solution: Given Information

  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 41 atm

the air heats up while being compressed, its pressure rises more than twenty-fold.

If the air is taken into the cylinder at 11C, how hot does it get after being compressed?

You are using centigrade for temperature . The formula is valid only when you use absolute scale of temperature .
Use 273+11 = 284K for T1
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T2/T1 = (P2/P1)*(V2/V1)

P2/P1 = 41
air is compressed to one twentieth of its original volume V2/V1 = 1/ 20

T2 = (41/20)*284 = 582.2 K

= 582-273 = 309.2° C answer

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