Posted by **CheckingMyAnswers** on Saturday, May 11, 2013 at 3:48am.

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

- ThermoPhysics -
**Elena**, Saturday, May 11, 2013 at 4:31am
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

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