> restart;#'therm_eq1.mws'.24-06-05.

Chapter 1: Set of pre-written equations available. (REM: use D for Delta instead of E2_E1).

Basic definition of thermodynamic work

 > eq1_1:=W=-Int(F[int],r);

Work of compression/expansion

 > eq1_2:=W=-Int(p,V);

Useful work (not accounting the atmosferic one, at p0)

 > eq1_3:=W[u]=W+p[0]*DV;

Definition of energy and energy balance for a control mass

 > eq1_4:=DE=W[Q=0];eq1_5:=DE=W+Q;

Definition of stored mechanical energy without friction

 > eq1_6:=DE[m]=(W+Int(p,V))[E[mdf]=0];

Definition of friction-dissipation energy and mechanical energy balance

 > eq1_7:=E[mdf]=W+Int(p,V)-DE[m];eq1_8:=W=solve(eq1_7,W);

Definition of internal energy and internal energy equation

 > eq1_9:=DU=DE-DE[m];eq1_10:=subs(DE[m]=DEm,eq1_5,eq1_8,DEm=DE[m],eq1_9);

Density and its equation of state in the ideal gas model and the ideal condensed model

 > eq1_11:=rho=m/V;eq1_12:=rho=p/(R*T);eq1_13:=R=R[u]/M;eq1_14:=p*V=subs(eq1_11,solve(eq1_12,p)*V);eq1_15:=rho=rho[0];

The energetic equation of state for perfec calorific substances (for condensed phases no distintion between c[v] and c[p])

 > eq1_16:=DU=m*c[v]*DT;eq1_17:=DU=m*c*DT;

Reminder of Mayer's relation and definition of the isentropic exponent

 > eq1_18:=c[p]-c[v]=R;eq1_19:=gamma=c[p]/c[v];

Adiabatic evolution of a perfect gas without friccion (isentropic evolution of a perfect gas). Can be deduced by eq1_2, eq1_4, eq1_13 and Q=0.

 > eq1_BEMCQ0F0:=m*c[v]*dT=0-p*dV;eq1_20:=p[1]*V[1]^gamma=p[2]*V[2]^gamma;eq1_21:=T[1]*V[1]^(gamma-1)=T[2]*V[2]^(gamma-1);eq1_22:=T[2]/T[1]=(p[2]/p[1])^((gamma-1)/gamma);

Momentum equation for a piston (force balance) and its first integral (mechanical energy balance)

 > eq1_23:=F=m[P]*diff(x(t),t,t);eq1_24:=Int(F,x=x1..x2)=m[P]*(diff(x(t),t)[x2]^2-diff(x(t),t)[x1]^2)/2;

Collection of all equations defined:

 > eq1_all:=[seq(cat(eq1_,i),i=1..3)]:[seq(cat(eq1_,i),i=1..3)]=%;

WARNING. A list of all variables follows, to copy and paste to the save command (after Maple7 there is no saving all). CAUTION: After pasting all, I must MANUALLY delete system variables: like RealRange_...

 > sort([anames()]);

 > #save eq1_1, eq1_10, eq1_11, eq1_12,eq1_13, eq1_14, eq1_15, eq1_16, eq1_17, eq1_18, eq1_19, eq1_2, eq1_20, eq1_21, eq1_22, eq1_23,eq1_24, eq1_3, eq1_4, eq1_5, eq1_6, eq1_7, eq1_8, eq1_9, "../therm_eq1.m":

HOW TO USE IT?

Example: Find the density of water vapor a 100 ÂșC and 100 kPa.

Solution:

There is not a direct procedure rho(T1,p1,substance1,ideal_gas_model) like in EES.

Here you must use Maple subs(T=T1,p=p1,dat,eq1_12), where dat is a list of data, including substance data, previously found by reading an internal data table, in that way: