Question

During the compression stroke of a certain gasoline engine, the pressure increases from 1.00 atm to 20.5 atm. The process is adiabatic and the air–fuel mixture behaves as a diatomic ideal gas.
(a) By what factor does the volume change?
Vfinal = Vinitial
(b) By what factor does the temperature change?
Tfinal = Tinitial
Assume the compression starts with 0.016 mole of gas at 26.5°C.
(c) Find the value of Q that characterizes the process.
J
(d) Find the value of ΔEint that characterizes the process.
J
(e) Find the value of W that characterizes the process.
J

Answer 1

Adiabatic index
γ=(i+2)/i=(5+2)/5= 1.4.
(a) p₁(V₁)^γ=p₂(V₂)^γ
V₁/V₂ =( p₂/p₁)^(1/ γ)=20.5^(1/1.4)=
=20.5^(0.714)=8.65.

(b) (p₂/p₁)^(γ-1) = (T₂/T₁)^γ
(T₂/T₁) =((p₂/p₁)^[(γ-1/γ)]=
=20.5^(0.2857)=2.37.

(c) An adiabatic process is a process occurring without exchange of heat of a system with its environment =>
Q=0.

ν =0.016 mol
T₁=273+26.5 = 299.5 K,
T₂/T₁=2.37,
T₂=2.37•T₁=2.37•299.5=710 K.

(d,e) ΔE=- W
W= ν•{R/(γ-1)}(T₁-T₂) =
=0.016•8.31(299.5-710)/(1.4-1) =
= - 136.45 J
ΔE=136.45 J