Arbejde

In the course of pumping up a bicycle tire, a liter of air at atmospheric pressure is compressed adiabatically to pressure of 7 atm. (Air is mostly diatomic nitrogen and oxygen).

(b) How much work is done in compressing the air?

Fra opgave a, "What is the final colume of this air after compression?" har jeg

V^γP = constant, hvor γ = (f + 2)/f dvs. frihedsgraden for diatomic i dette tilfælde er 5.

V₂ = V₁(P₂/P₁)^(-1/γ) ≈ 0.25 L

så nu med opg b, vil jeg bruge den samme formel - omskrevet at P = (V₁/V)^γP₁

W = - _V1∫^V2 P dV = - V₁^γP_{1 V1}∫^V2 (1/V^γ) dV = -1^7/5·1.013·10⁵₁∫^0.25 (1/V^7/5) dV = 187684 J ≈ 188 kJ

Men min lærer skrev, at det skulle være 188 J. Hvorfor?