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 56 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 22?C, how hot does it get after being compressed?
Answer in units of ?C.

Explanation / Answer

Use the combined gas law

P1V1/T1 = P2V2/T2
(1 atm)(1 V)/(22+273.15K) = (56 atm)(1/20 V)/T
1/(295.15K)=(56/20) / T
1/(295.15)=(2.8) / T
T = (295.15)(2.8)

T = 826.42K

T - 273.15 = T in degrees C

826.42 - 273.15K = 553.27 degrees C

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.