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 Need Help??

Every afternoon I produce tea for the local barbarians (Dutch, Belgium). Of course this involves warming the pot. The other day I had an extra guest for tea so I could not use as much water as usual for warming. What warming water I could spare I used in two steps claiming this would be more efficient. The Dutch dissented so I did what any sane monk would do and wrote a script ...

```#/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 );
}

Here are some results

```********** 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

The physics model sucks so the numbers are not true but I think the broad conclusion is valid. Now can anyone suggest a nice 3 axis plotting module so I can plot the pot warming space ?

Cheers,
R.

Pereant, qui ante nos nostra dixerunt!

In reply to Warming the pot by Random_Walk

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