The ice at zero did four times the work of water at zero

# Self-authored for the EML case corpus (no external origin). A host chilling
# drinks has ice at zero degrees and iced water at zero degrees, reasons that
# two things at the same temperature cool the same, pours the water in to
# avoid dilution, and the drinks stay warm. What a hundred grams at zero can
# absorb, as ice and as water, is computed below.
#
# The reasoning is careful. Both are at exactly zero; a thermometer cannot tell
# them apart; cooling flows from cold to warm; and the intent was exactly 'cool
# the drink as much as the cold thing can'.
#
# Melting absorbs heat without any change of temperature, 334 joules per gram,
# while warming water absorbs 4.2 joules per gram per degree - so a hundred
# grams of ice takes 33400 joules just to become water at zero and then warms
# like water, five times what the same hundred grams of zero-degree water can
# take on its way to twenty.

100 => cooler_mass_g
334 => latent_heat_of_melting_j_per_g
42 => specific_heat_of_water_tenths_of_a_j_per_g_k
20 => drink_start_c
500 => drink_mass_g

int(cooler_mass_g * specific_heat_of_water_tenths_of_a_j_per_g_k * drink_start_c / 10) => water_at_zero_can_absorb_warming_to_twenty_j
cooler_mass_g * latent_heat_of_melting_j_per_g => ice_absorbs_while_melting_j
ice_absorbs_while_melting_j + water_at_zero_can_absorb_warming_to_twenty_j => ice_can_absorb_in_all_to_twenty_j
int(ice_can_absorb_in_all_to_twenty_j * 100 / water_at_zero_can_absorb_warming_to_twenty_j) => ice_over_water_per_hundred
int(ice_absorbs_while_melting_j * 100 / water_at_zero_can_absorb_warming_to_twenty_j) => melting_alone_over_water_per_hundred

int(drink_mass_g * specific_heat_of_water_tenths_of_a_j_per_g_k / 10) => drink_heat_capacity_j_per_k
int(cooler_mass_g * specific_heat_of_water_tenths_of_a_j_per_g_k / 10) => cooler_heat_capacity_j_per_k
int(drink_heat_capacity_j_per_k * drink_start_c * 10 / (drink_heat_capacity_j_per_k + cooler_heat_capacity_j_per_k)) => final_temperature_with_water_tenths_c
int((drink_heat_capacity_j_per_k * drink_start_c - ice_absorbs_while_melting_j) * 10 / (drink_heat_capacity_j_per_k + cooler_heat_capacity_j_per_k)) => final_temperature_with_ice_tenths_c
final_temperature_with_water_tenths_c - final_temperature_with_ice_tenths_c => extra_cooling_from_the_ice_tenths_c
drink_start_c * 10 - final_temperature_with_water_tenths_c => cooling_from_the_water_tenths_c
drink_start_c * 10 - final_temperature_with_ice_tenths_c => cooling_from_the_ice_tenths_c

"cooler                          : " + str(cooler_mass_g) + " g at 0 C, as water or as ice" ^0
"drink                           : " + str(drink_mass_g) + " g at " + str(drink_start_c) + " C" ^0
"" ^0
"water at zero can absorb        : " + str(water_at_zero_can_absorb_warming_to_twenty_j) + " J warming to " + str(drink_start_c) + " C" ^0
"ice absorbs while melting       : " + str(ice_absorbs_while_melting_j) + " J, at zero the whole time" ^0
"ice can absorb in all           : " + str(ice_can_absorb_in_all_to_twenty_j) + " J to " + str(drink_start_c) + " C" ^0
"ice over water                  : " + str(ice_over_water_per_hundred) + " per hundred; the melting alone is " + str(melting_alone_over_water_per_hundred) ^0
"" ^0
"drink with the water            : ends at " + str(final_temperature_with_water_tenths_c) + " tenths of a degree, cooled " + str(cooling_from_the_water_tenths_c) + " tenths" ^0
"drink with the ice              : ends at " + str(final_temperature_with_ice_tenths_c) + " tenths of a degree, cooled " + str(cooling_from_the_ice_tenths_c) + " tenths" ^0
"extra cooling from the ice      : " + str(extra_cooling_from_the_ice_tenths_c) + " tenths of a degree" ^0
"" ^0

# ---- what the host verified ----

"the same-temperature reasoning" ^0
"  ice : 0 C" ^0
"  water : 0 C" ^0
"  thermometer : cannot tell them apart" ^0
"  intent : cool the drink as much as the cold thing can" ^0
"  facts wrong : 0" ^0
"  verdict : SAME TEMPERATURE, SAME COOLING" ^0
"" ^0
"  checking both at exactly zero is the part done right here," ^0
"  and it is why the first joule of heat flows into each of" ^0
"  them at exactly the same rate" ^0
"" ^0

# ---- what a hundred grams at zero can absorb ----

"temperature is not capacity" ^0
"  what temperature says : which way heat flows, and how fast" ^0
"  what it does not say : how much heat a thing can take" ^0
"  water at zero : takes " + str(specific_heat_of_water_tenths_of_a_j_per_g_k) + " tenths of a joule per gram per degree, and" ^0
"    is at the drink's temperature after " + str(water_at_zero_can_absorb_warming_to_twenty_j) + " J" ^0
"  ice at zero : takes " + str(latent_heat_of_melting_j_per_g) + " J per gram to melt, staying at zero," ^0
"    " + str(ice_absorbs_while_melting_j) + " J before it even starts to warm" ^0
"  the same reading, " + str(ice_over_water_per_hundred) + " per hundred of the work : because a change" ^0
"    of state absorbs heat that a thermometer never sees" ^0
"" ^0

# ---- what the host got ----

"the drinks" ^0
"  believed : cooled as much as ice would, with no dilution" ^0
"  actual : " + str(cooling_from_the_water_tenths_c) + " tenths of a degree cooler, where ice gives " + str(cooling_from_the_ice_tenths_c) ^0
"  is the thermometer wrong : no; both really are at zero" ^0
"  is temperature the measure of cooling power : no; the" ^0
"    melting is where the ice does its work, at zero, unseen" ^0
"" ^0

# ---- null control ----

# The same choice made on heat absorbed instead of on temperature read.
8400 => nc_cooling_power_read_from_temperature_j
41800 => nc_cooling_power_read_from_heat_absorbed_j
33400 => nc_joules_the_change_of_state_hides

"null control - measure what each can absorb" ^0
"  cooling power, read from temperature : " + str(nc_cooling_power_read_from_temperature_j) + " J, the same for both" ^0
"  cooling power, read from heat absorbed : " + str(nc_cooling_power_read_from_heat_absorbed_j) + " J for the ice" ^0
"  joules the change of state hides : " + str(nc_joules_the_change_of_state_hides) ^0
"  no ice and no drink changed; the capacity was measured" ^0
"  instead of the temperature" ^0
"" ^0

# ---- the rule ----

"what two things at the same temperature guarantee" ^0
"  heat flows into each at the same rate at first : exactly" ^0
"  each can absorb the same amount : not addressed; ice absorbs" ^0
"    " + str(ice_absorbs_while_melting_j) + " J in melting with no change of temperature, so " + str(cooler_mass_g) + " g of" ^0
"    ice at zero takes " + str(ice_over_water_per_hundred) + " per hundred of what " + str(cooler_mass_g) + " g of water at zero can" ^0
"" ^0

"a thermometer reads the doorway and not the room; ice and water at zero" ^0
"stand at the same door, and one of them has a hall behind it that swallows" ^0
"heat without moving the needle" ^0
"" ^0

"Both are at zero - the thermometer is right. But temperature is direction," ^0
"not capacity: melting takes " + str(ice_absorbs_while_melting_j) + " J with no change of reading, so the ice can" ^0
"absorb " + str(ice_can_absorb_in_all_to_twenty_j) + " J against the water's " + str(water_at_zero_can_absorb_warming_to_twenty_j) + ", cooling the drink " + str(cooling_from_the_ice_tenths_c) + " tenths of a degree" ^0
"where the water manages " + str(cooling_from_the_water_tenths_c) + ", until the cold thing is measured by what it can absorb." ^0

cooler_mass_g = 100
latent_heat_of_melting_j_per_g = 334
specific_heat_of_water_tenths_of_a_j_per_g_k = 42
drink_start_c = 20
drink_mass_g = 500
water_at_zero_can_absorb_warming_to_twenty_j = int(cooler_mass_g * specific_heat_of_water_tenths_of_a_j_per_g_k * drink_start_c / 10)
ice_absorbs_while_melting_j = cooler_mass_g * latent_heat_of_melting_j_per_g
ice_can_absorb_in_all_to_twenty_j = ice_absorbs_while_melting_j + water_at_zero_can_absorb_warming_to_twenty_j
ice_over_water_per_hundred = int(ice_can_absorb_in_all_to_twenty_j * 100 / water_at_zero_can_absorb_warming_to_twenty_j)
melting_alone_over_water_per_hundred = int(ice_absorbs_while_melting_j * 100 / water_at_zero_can_absorb_warming_to_twenty_j)
drink_heat_capacity_j_per_k = int(drink_mass_g * specific_heat_of_water_tenths_of_a_j_per_g_k / 10)
cooler_heat_capacity_j_per_k = int(cooler_mass_g * specific_heat_of_water_tenths_of_a_j_per_g_k / 10)
final_temperature_with_water_tenths_c = int(drink_heat_capacity_j_per_k * drink_start_c * 10 / (drink_heat_capacity_j_per_k + cooler_heat_capacity_j_per_k))
final_temperature_with_ice_tenths_c = int((drink_heat_capacity_j_per_k * drink_start_c - ice_absorbs_while_melting_j) * 10 / (drink_heat_capacity_j_per_k + cooler_heat_capacity_j_per_k))
extra_cooling_from_the_ice_tenths_c = final_temperature_with_water_tenths_c - final_temperature_with_ice_tenths_c
cooling_from_the_water_tenths_c = drink_start_c * 10 - final_temperature_with_water_tenths_c
cooling_from_the_ice_tenths_c = drink_start_c * 10 - final_temperature_with_ice_tenths_c
print("cooler                          : " + str(cooler_mass_g) + " g at 0 C, as water or as ice")
print("drink                           : " + str(drink_mass_g) + " g at " + str(drink_start_c) + " C")
print("")
print("water at zero can absorb        : " + str(water_at_zero_can_absorb_warming_to_twenty_j) + " J warming to " + str(drink_start_c) + " C")
print("ice absorbs while melting       : " + str(ice_absorbs_while_melting_j) + " J, at zero the whole time")
print("ice can absorb in all           : " + str(ice_can_absorb_in_all_to_twenty_j) + " J to " + str(drink_start_c) + " C")
print("ice over water                  : " + str(ice_over_water_per_hundred) + " per hundred; the melting alone is " + str(melting_alone_over_water_per_hundred))
print("")
print("drink with the water            : ends at " + str(final_temperature_with_water_tenths_c) + " tenths of a degree, cooled " + str(cooling_from_the_water_tenths_c) + " tenths")
print("drink with the ice              : ends at " + str(final_temperature_with_ice_tenths_c) + " tenths of a degree, cooled " + str(cooling_from_the_ice_tenths_c) + " tenths")
print("extra cooling from the ice      : " + str(extra_cooling_from_the_ice_tenths_c) + " tenths of a degree")
print("")
print("the same-temperature reasoning")
print("  ice : 0 C")
print("  water : 0 C")
print("  thermometer : cannot tell them apart")
print("  intent : cool the drink as much as the cold thing can")
print("  facts wrong : 0")
print("  verdict : SAME TEMPERATURE, SAME COOLING")
print("")
print("  checking both at exactly zero is the part done right here,")
print("  and it is why the first joule of heat flows into each of")
print("  them at exactly the same rate")
print("")
print("temperature is not capacity")
print("  what temperature says : which way heat flows, and how fast")
print("  what it does not say : how much heat a thing can take")
print("  water at zero : takes " + str(specific_heat_of_water_tenths_of_a_j_per_g_k) + " tenths of a joule per gram per degree, and")
print("    is at the drink's temperature after " + str(water_at_zero_can_absorb_warming_to_twenty_j) + " J")
print("  ice at zero : takes " + str(latent_heat_of_melting_j_per_g) + " J per gram to melt, staying at zero,")
print("    " + str(ice_absorbs_while_melting_j) + " J before it even starts to warm")
print("  the same reading, " + str(ice_over_water_per_hundred) + " per hundred of the work : because a change")
print("    of state absorbs heat that a thermometer never sees")
print("")
print("the drinks")
print("  believed : cooled as much as ice would, with no dilution")
print("  actual : " + str(cooling_from_the_water_tenths_c) + " tenths of a degree cooler, where ice gives " + str(cooling_from_the_ice_tenths_c))
print("  is the thermometer wrong : no; both really are at zero")
print("  is temperature the measure of cooling power : no; the")
print("    melting is where the ice does its work, at zero, unseen")
print("")
nc_cooling_power_read_from_temperature_j = 8400
nc_cooling_power_read_from_heat_absorbed_j = 41800
nc_joules_the_change_of_state_hides = 33400
print("null control - measure what each can absorb")
print("  cooling power, read from temperature : " + str(nc_cooling_power_read_from_temperature_j) + " J, the same for both")
print("  cooling power, read from heat absorbed : " + str(nc_cooling_power_read_from_heat_absorbed_j) + " J for the ice")
print("  joules the change of state hides : " + str(nc_joules_the_change_of_state_hides))
print("  no ice and no drink changed; the capacity was measured")
print("  instead of the temperature")
print("")
print("what two things at the same temperature guarantee")
print("  heat flows into each at the same rate at first : exactly")
print("  each can absorb the same amount : not addressed; ice absorbs")
print("    " + str(ice_absorbs_while_melting_j) + " J in melting with no change of temperature, so " + str(cooler_mass_g) + " g of")
print("    ice at zero takes " + str(ice_over_water_per_hundred) + " per hundred of what " + str(cooler_mass_g) + " g of water at zero can")
print("")
print("a thermometer reads the doorway and not the room; ice and water at zero")
print("stand at the same door, and one of them has a hall behind it that swallows")
print("heat without moving the needle")
print("")
print("Both are at zero - the thermometer is right. But temperature is direction,")
print("not capacity: melting takes " + str(ice_absorbs_while_melting_j) + " J with no change of reading, so the ice can")
print("absorb " + str(ice_can_absorb_in_all_to_twenty_j) + " J against the water's " + str(water_at_zero_can_absorb_warming_to_twenty_j) + ", cooling the drink " + str(cooling_from_the_ice_tenths_c) + " tenths of a degree")
print("where the water manages " + str(cooling_from_the_water_tenths_c) + ", until the cold thing is measured by what it can absorb.")

cooler                          : 100 g at 0 C, as water or as ice
drink                           : 500 g at 20 C

water at zero can absorb        : 8400 J warming to 20 C
ice absorbs while melting       : 33400 J, at zero the whole time
ice can absorb in all           : 41800 J to 20 C
ice over water                  : 497 per hundred; the melting alone is 397

drink with the water            : ends at 166 tenths of a degree, cooled 34 tenths
drink with the ice              : ends at 34 tenths of a degree, cooled 166 tenths
extra cooling from the ice      : 132 tenths of a degree

the same-temperature reasoning
  ice : 0 C
  water : 0 C
  thermometer : cannot tell them apart
  intent : cool the drink as much as the cold thing can
  facts wrong : 0
  verdict : SAME TEMPERATURE, SAME COOLING

  checking both at exactly zero is the part done right here,
  and it is why the first joule of heat flows into each of
  them at exactly the same rate

temperature is not capacity
  what temperature says : which way heat flows, and how fast
  what it does not say : how much heat a thing can take
  water at zero : takes 42 tenths of a joule per gram per degree, and
    is at the drink's temperature after 8400 J
  ice at zero : takes 334 J per gram to melt, staying at zero,
    33400 J before it even starts to warm
  the same reading, 497 per hundred of the work : because a change
    of state absorbs heat that a thermometer never sees

the drinks
  believed : cooled as much as ice would, with no dilution
  actual : 34 tenths of a degree cooler, where ice gives 166
  is the thermometer wrong : no; both really are at zero
  is temperature the measure of cooling power : no; the
    melting is where the ice does its work, at zero, unseen

null control - measure what each can absorb
  cooling power, read from temperature : 8400 J, the same for both
  cooling power, read from heat absorbed : 41800 J for the ice
  joules the change of state hides : 33400
  no ice and no drink changed; the capacity was measured
  instead of the temperature

what two things at the same temperature guarantee
  heat flows into each at the same rate at first : exactly
  each can absorb the same amount : not addressed; ice absorbs
    33400 J in melting with no change of temperature, so 100 g of
    ice at zero takes 497 per hundred of what 100 g of water at zero can

a thermometer reads the doorway and not the room; ice and water at zero
stand at the same door, and one of them has a hall behind it that swallows
heat without moving the needle

Both are at zero - the thermometer is right. But temperature is direction,
not capacity: melting takes 33400 J with no change of reading, so the ice can
absorb 41800 J against the water's 8400, cooling the drink 166 tenths of a degree
where the water manages 34, until the cold thing is measured by what it can absorb.

Trace event types