//http://www.timestocome.com
//linda cobb
//winter 98-99



//solve coffee cooling problem using euler method
//is it better to add cream first or later to cool 
//coffee quickly?


//temperatures are in C

#include <math.h>
#include <stdio.h>

#define TIMESTEP  0.001

void main (void){


  //try to solve T-Ts = c(exp)^(-rt)

  double   Ts=20;             //room temperature
  double   Told;              //begining temperature of coffee
  double   t = 0.0;           //begining time
  double   r;                 //estimated cooling constant
  double   h;                 //time step
  double   Tnew;              //new temperature
  double   C;                 //constant of integration (T-Ts)
  int      j=0;


  //black coffee
  h = TIMESTEP;
  r = 0.027;
  C = 62.3;
  Told = 90.0;
  Tnew = 90.0;
  
  printf("\n Black Coffee \n");

  while(Tnew >= 80.0){          //cool enough to drink at 75'

    if(t < TIMESTEP){
      Tnew = Told;
    }else{
      Tnew =  Told - h*r*(Told-Ts);    
    } 
        t += TIMESTEP;  
	Told = Tnew;

        j+=1; 
        if(j >= 1000 ){
      	printf("\n minutes passed = %d, Temp = %.1f ",(int)t, Tnew);
	j = 0;
      }








	if(Tnew <= 80.0){
	  Tnew -= 5;
	  printf("\n added cream at %.1f minutes, now the temperature is %.1f", t,Tnew);
	}
   }
  printf("\n+++++++++++++++++++++++++++++++++");
 
  //coffee w/ cream
  r = 0.025;
  C = 48.8;
  Told = 90.0 - 5.0;                   //cream cools coffee by 5'
  Tnew = 90.0 - 5.0;
  t = 0.0;
  j = 0;

  printf("\n Coffee w/ cream\n");

  while(Tnew >= 75){

    if(t < TIMESTEP){
      Tnew = Told;
    }else{
      Tnew = Told - h*r*(Told-Ts);    //previous value - timestep*dF/dt
    }
        t+= TIMESTEP;
        Told = Tnew;
        
        j+=1;
	if(j >= 1000){
	  printf("\n minutes passed = %.1f, Temp = %.1f ",t, Tnew);
	  j=0;
	}
  } 
  printf( "\n coffee w/ cream cool enough to drink at %.1f minutes, at a temperature of %.1f", t, Tnew);
  printf ("\n\n");

}