#/usr/bin/perl
use strict;
use warnings;
# Teapot warming with various splits of water from 10 to 200 ml
#
# wild assumptions:
#    pot and warming fraction are allowed to reach equilibrium tempera
+ture
#    pot heat loss between warmings is just a random guess
#    pot specific heat capacity is a wild guess
#    warming water is always 100 Celsius
#    entire pot is one temperature
#   temperatures handled in Celsius not Kelvin, assume this makes no o
+dds
#   assumed heat capacities are linear
#

# heat capacity joules per Kelvin for 1 teapot or 1 gram water
my %hc = (
    pot   => 1500,
    water => 4.2
);
my $T_env       = 20;      # Celsius
my $T_water     = 100;     # Celsius
my $total_water = 1500;    # ml
my $cool_factor = 0.05;

{
    printf "********** the evil of an unwarmed pot ... ";
    my $T_tea = warm_pot( $T_env, $total_water, );
    printf "temp tea: %5.2fC ********** \n\n", $T_tea;
}                          
for my $warming_water ( 1 .. 10 ) {
    $warming_water *= 10;
    my $T_pot = $T_env;

    # we split the water into various fractions
    my $max_step = 4;
    for my $split ( 1 .. $max_step ) {
        my $ml = $warming_water / $split;
        printf
          "warming with $warming_water in %2i steps (%5.1f water each 
+step) ",
          $split, $ml;
        for ( 1 .. $split ) {
            $T_pot = warm_pot( $T_pot, $ml );
            print ".";
        }

        print " " x ( 1 + $max_step - $split );
        printf "warmed pot: %5.2fC ", $T_pot;
        $T_pot = cools($T_pot);

        # now throw in 1500 ml hot water
        my $T_tea = warm_pot( $T_pot, $total_water - $warming_water, )
+;
        printf "temp tea: %5.2fC\n", $T_tea;
    }
    print $/;
}

sub warm_pot {
    my $T_pot  = shift;
    my $ml_h2o = shift;

    my $total_joules = $T_pot * $hc{pot} + $ml_h2o * $hc{water} * $T_w
+ater;
    my $total_heat_capacity = $hc{pot} + $ml_h2o * $hc{water};
    return $total_joules / $total_heat_capacity;
}

sub cools {
    my $T_pot   = shift;
    my $delta_T = $T_pot - $T_env;
    return $T_pot - ( $delta_T * $cool_factor );
}
[download]

********** the evil of an unwarmed pot ... initial temp tea: 84.62C **
+******** 

using 10ml in 1 steps  10.0 water each .    warmed pot: 22.18C temp te
+a: 84.93C
using 10ml in 2 steps   5.0 water each ..   warmed pot: 24.21C temp te
+a: 85.30C
using 10ml in 3 steps   3.3 water each ...  warmed pot: 26.09C temp te
+a: 85.65C
using 10ml in 4 steps   2.5 water each .... warmed pot: 27.82C temp te
+a: 85.97C
.
.
.
using 60ml in 1 steps  60.0 water each .    warmed pot: 31.51C temp te
+a: 86.27C
using 60ml in 2 steps  30.0 water each ..   warmed pot: 41.22C temp te
+a: 88.11C
using 60ml in 3 steps  20.0 water each ...  warmed pot: 49.18C temp te
+a: 89.61C
using 60ml in 4 steps  15.0 water each .... warmed pot: 55.66C temp te
+a: 90.83C

using 70ml in 1 steps  70.0 water each .    warmed pot: 33.11C temp te
+a: 86.50C
using 70ml in 2 steps  35.0 water each ..   warmed pot: 43.97C temp te
+a: 88.56C
using 70ml in 3 steps  23.3 water each ...  warmed pot: 52.67C temp te
+a: 90.22C
using 70ml in 4 steps  17.5 water each .... warmed pot: 59.56C temp te
+a: 91.52C

using 80ml in 1 steps  80.0 water each .    warmed pot: 34.64C temp te
+a: 86.72C
using 80ml in 2 steps  40.0 water each ..   warmed pot: 46.55C temp te
+a: 88.99C
using 80ml in 3 steps  26.7 water each ...  warmed pot: 55.87C temp te
+a: 90.77C
using 80ml in 4 steps  20.0 water each .... warmed pot: 63.07C temp te
+a: 92.15C

using 90ml in 1 steps  90.0 water each .    warmed pot: 36.10C temp te
+a: 86.92C
using 90ml in 2 steps  45.0 water each ..   warmed pot: 48.97C temp te
+a: 89.39C
using 90ml in 3 steps  30.0 water each ...  warmed pot: 58.80C temp te
+a: 91.28C
using 90ml in 4 steps  22.5 water each .... warmed pot: 66.21C temp te
+a: 92.70C

using 100ml in 1 steps 100.0 water each .    warmed pot: 37.50C temp t
+ea: 87.12C
using 100ml in 2 steps  50.0 water each ..   warmed pot: 51.23C temp t
+ea: 89.77C
using 100ml in 3 steps  33.3 water each ...  warmed pot: 61.49C temp t
+ea: 91.75C
using 100ml in 4 steps  25.0 water each .... warmed pot: 69.04C temp t
+ea: 93.21C

using 110ml in 1 steps 110.0 water each .    warmed pot: 38.84C temp t
+ea: 87.30C
using 110ml in 2 steps  55.0 water each ..   warmed pot: 53.37C temp t
+ea: 90.13C
using 110ml in 3 steps  36.7 water each ...  warmed pot: 63.97C temp t
+ea: 92.19C
using 110ml in 4 steps  27.5 water each .... warmed pot: 71.59C temp t
+ea: 93.66C

using 120ml in 1 steps 120.0 water each .    warmed pot: 40.12C temp t
+ea: 87.48C
using 120ml in 2 steps  60.0 water each ..   warmed pot: 55.37C temp t
+ea: 90.46C
using 120ml in 3 steps  40.0 water each ...  warmed pot: 66.26C temp t
+ea: 92.59C
using 120ml in 4 steps  30.0 water each .... warmed pot: 73.89C temp t
+ea: 94.08C

.
.
.
using 200ml in 1 steps 200.0 water each .    warmed pot: 48.72C temp t
+ea: 88.64C
using 200ml in 2 steps 100.0 water each ..   warmed pot: 67.82C temp t
+ea: 92.55C
using 200ml in 3 steps  66.7 water each ...  warmed pot: 79.31C temp t
+ea: 94.90C
using 200ml in 4 steps  50.0 water each .... warmed pot: 86.00C temp t
+ea: 96.27C
.
.
.
using 300ml in 1 steps 300.0 water each .    warmed pot: 56.52C temp t
+ea: 89.61C
using 300ml in 2 steps 150.0 water each ..   warmed pot: 77.53C temp t
+ea: 94.19C
using 300ml in 3 steps 100.0 water each ...  warmed pot: 87.91C temp t
+ea: 96.45C
using 300ml in 4 steps  75.0 water each .... warmed pot: 92.78C temp t
+ea: 97.51C
[download]