Example 11.4-6 Adiabatic Frictionless Processes in an ideal Gas > restart; > eq:=rho(t)*Cphat*D(T)(t)-D(p)(t); Eq. 11.4-53. > rho:=t->p(t)*MW/(Rgas*T(t)); Ideal gas law. > Cphat:=Cptil/MW; > eq:=simplify(eq/p(t)); equivalent to eq. 11.4-54 > simplify(eq-diff(Cptil*log(T(t))/Rgas-log(p(t)),t)); > p:=t->T(t)^(Cptil/Rgas)/Con; eq. 11.4-55 > eq; This satisfies our equation. > Cvtil:=Cptil-Rgas; For an ideal gas. See pages 436-7 of Reklaitis. > eq1:=gam=Cptil/Cvtil; Defining gamma > Cptil:=solve(eq1,Cptil); Cp on a mass basis is Cpmol/MW. > simplify(p(t)^((gam-1)/gam)/T(t),assume=positive); checking eq. 11.4-56. Looks good, but Maple can be very picky.
> gam:=0.25; > simplify(p(t)^((gam-1)/gam)/T(t),assume=positive); Very close to being constant.
> gam:='gam'; > eq57:=simplify(p(t)/rho(t)^gam,assume=positive); checking 11.4-57. It looks OK too.
> gam:=0.25; > simplify(eq57,assume=positive); This is also very close to being constant. > f:=x->c*x^(1333333333/4000000000)/x^(3333333333/10000000000); >