# Example 996 — The methane burned into nearly three times its mass `the_methane_burned_into_nearly_three_times_its_mass.eml` - A household burns 1000 kg of natural gas - methane - in a year, and a report says that makes 2750 kg of carbon dioxide. A neighbour objects: mass is conserved, so burning 1000 kg of gas cannot produce more than 1000 kg of anything. What burning really produces is computed below. ## EML ```eml # Self-authored for the EML case corpus (no external origin). A household burns # 1000 kg of natural gas - methane - in a year, and a report says that makes 2750 # kg of carbon dioxide. A neighbour objects: mass is conserved, so burning 1000 # kg of gas cannot produce more than 1000 kg of anything. What burning really # produces is computed below. # # The reasoning is careful. Mass really is conserved in burning; 1000 kg of # methane really was burned; the carbon dioxide really does come from that # methane's carbon; and the intent is exactly 'how much carbon dioxide'. # # Burning is a reaction with oxygen from the air: each 16 g of methane takes 64 g # of oxygen and gives 44 g of carbon dioxide and 36 g of water. The fuel's 1000 # kg take 4000 kg of oxygen with them, and the 5000 kg of products include 2750 # of carbon dioxide - mass is conserved, just not the mass the neighbour counted. 1000 => methane_burned_kg 12 => carbon_g_per_mole 1 => hydrogen_g_per_mole 16 => oxygen_g_per_mole carbon_g_per_mole + 4 * hydrogen_g_per_mole => methane_g_per_mole 2 * oxygen_g_per_mole => oxygen_molecule_g_per_mole carbon_g_per_mole + 2 * oxygen_g_per_mole => carbon_dioxide_g_per_mole 2 * hydrogen_g_per_mole + oxygen_g_per_mole => water_g_per_mole 2 * oxygen_molecule_g_per_mole => oxygen_used_per_mole_of_methane_g 2 * water_g_per_mole => water_made_per_mole_of_methane_g int(methane_burned_kg * oxygen_used_per_mole_of_methane_g / methane_g_per_mole) => oxygen_taken_from_the_air_kg int(methane_burned_kg * carbon_dioxide_g_per_mole / methane_g_per_mole) => carbon_dioxide_made_kg int(methane_burned_kg * water_made_per_mole_of_methane_g / methane_g_per_mole) => water_made_kg methane_burned_kg + oxygen_taken_from_the_air_kg => mass_going_in_kg carbon_dioxide_made_kg + water_made_kg => mass_coming_out_kg int(carbon_dioxide_made_kg * 100 / methane_burned_kg) => carbon_dioxide_vs_fuel_per_hundred "molecule masses : methane " + str(methane_g_per_mole) + ", oxygen " + str(oxygen_molecule_g_per_mole) + ", carbon dioxide " + str(carbon_dioxide_g_per_mole) + ", water " + str(water_g_per_mole) ^0 "per " + str(methane_g_per_mole) + " g of methane : takes " + str(oxygen_used_per_mole_of_methane_g) + " g of oxygen, gives " + str(carbon_dioxide_g_per_mole) + " g of carbon dioxide and " + str(water_made_per_mole_of_methane_g) + " g of water" ^0 "" ^0 "methane burned : " + str(methane_burned_kg) + " kg" ^0 "oxygen taken from the air : " + str(oxygen_taken_from_the_air_kg) + " kg" ^0 "mass going in : " + str(mass_going_in_kg) + " kg" ^0 "carbon dioxide made : " + str(carbon_dioxide_made_kg) + " kg, " + str(carbon_dioxide_vs_fuel_per_hundred) + " per hundred of the fuel" ^0 "water made : " + str(water_made_kg) + " kg" ^0 "mass coming out : " + str(mass_coming_out_kg) + " kg" ^0 "" ^0 # ---- what the neighbour verified ---- "the conservation reasoning" ^0 " law : mass is conserved in burning" ^0 " fuel : " + str(methane_burned_kg) + " kg of methane" ^0 " source of the carbon : the methane, and nothing else" ^0 " intent : how much carbon dioxide" ^0 " facts wrong : 0" ^0 " verdict : NO MORE THAN " + str(methane_burned_kg) + " KG OF ANYTHING CAN COME OUT" ^0 "" ^0 " holding to the conservation of mass is the part done right" ^0 " here, and it is why what goes in and what comes out must weigh" ^0 " the same" ^0 "" ^0 # ---- what burning takes in ---- "the unweighed ingredient" ^0 " what burning is : methane combining with oxygen from the air" ^0 " per molecule of methane : two of oxygen, " + str(oxygen_used_per_mole_of_methane_g) + " g for every " + str(methane_g_per_mole) + " g of fuel" ^0 " what goes in : " + str(methane_burned_kg) + " kg of fuel and " + str(oxygen_taken_from_the_air_kg) + " kg of oxygen, " + str(mass_going_in_kg) + " kg" ^0 " what comes out : " + str(carbon_dioxide_made_kg) + " kg of carbon dioxide and " + str(water_made_kg) + " kg of water," ^0 " " + str(mass_coming_out_kg) + " kg - conserved to the kilogram" ^0 " why the carbon dioxide outweighs the fuel : each carbon atom" ^0 " leaves with two oxygen atoms that were never in the fuel" ^0 "" ^0 # ---- what the neighbour got ---- "the objection" ^0 " believed : at most " + str(methane_burned_kg) + " kg of carbon dioxide" ^0 " actual : " + str(carbon_dioxide_made_kg) + " kg" ^0 " is the conservation of mass wrong : no; " + str(mass_going_in_kg) + " kg in, " + str(mass_coming_out_kg) + " kg out" ^0 " is the fuel all that goes in : no; the air supplies four times" ^0 " its mass in oxygen" ^0 "" ^0 # ---- null control ---- # The same year's burning weighed with the oxygen from the air counted in. 1000 => nc_carbon_dioxide_capped_at_the_fuel_kg 2750 => nc_carbon_dioxide_counting_the_air_kg 1750 => nc_kg_the_air_adds "null control - weigh the air too" ^0 " carbon dioxide, capped at the fuel's mass : " + str(nc_carbon_dioxide_capped_at_the_fuel_kg) + " kg" ^0 " carbon dioxide, counting the oxygen from the air : " + str(nc_carbon_dioxide_counting_the_air_kg) + " kg" ^0 " kg the air adds : " + str(nc_kg_the_air_adds) ^0 " no fuel and no flame changed; everything that entered the" ^0 " reaction was put on the scale" ^0 "" ^0 # ---- the rule ---- "what the conservation of mass guarantees" ^0 " what comes out of the flame weighs what went in : exactly" ^0 " the carbon dioxide weighs no more than the fuel : not addressed;" ^0 " oxygen from the air goes in too, " + str(oxygen_taken_from_the_air_kg) + " kg of it, and the " + str(methane_burned_kg) + " kg of" ^0 " methane come out as " + str(carbon_dioxide_made_kg) + " kg of carbon dioxide and " + str(water_made_kg) + " of water" ^0 "" ^0 "a law of conservation balances every account, including the ones nobody" ^0 "opened; the flame draws from the air, and the air's share arrives in the" ^0 "smoke" ^0 "" ^0 "Mass is conserved - " + str(mass_going_in_kg) + " kg in, " + str(mass_coming_out_kg) + " kg out. But the fuel is not all that" ^0 "goes in: " + str(methane_burned_kg) + " kg of methane take " + str(oxygen_taken_from_the_air_kg) + " kg of oxygen from the air, and each carbon" ^0 "atom leaves with two oxygen atoms, so the year's burning makes " + str(carbon_dioxide_made_kg) + " kg of carbon" ^0 "dioxide, until the air is put on the scale with the fuel." ^0 ``` ## Python (deterministic transpilation) ```python methane_burned_kg = 1000 carbon_g_per_mole = 12 hydrogen_g_per_mole = 1 oxygen_g_per_mole = 16 methane_g_per_mole = carbon_g_per_mole + 4 * hydrogen_g_per_mole oxygen_molecule_g_per_mole = 2 * oxygen_g_per_mole carbon_dioxide_g_per_mole = carbon_g_per_mole + 2 * oxygen_g_per_mole water_g_per_mole = 2 * hydrogen_g_per_mole + oxygen_g_per_mole oxygen_used_per_mole_of_methane_g = 2 * oxygen_molecule_g_per_mole water_made_per_mole_of_methane_g = 2 * water_g_per_mole oxygen_taken_from_the_air_kg = int(methane_burned_kg * oxygen_used_per_mole_of_methane_g / methane_g_per_mole) carbon_dioxide_made_kg = int(methane_burned_kg * carbon_dioxide_g_per_mole / methane_g_per_mole) water_made_kg = int(methane_burned_kg * water_made_per_mole_of_methane_g / methane_g_per_mole) mass_going_in_kg = methane_burned_kg + oxygen_taken_from_the_air_kg mass_coming_out_kg = carbon_dioxide_made_kg + water_made_kg carbon_dioxide_vs_fuel_per_hundred = int(carbon_dioxide_made_kg * 100 / methane_burned_kg) print("molecule masses : methane " + str(methane_g_per_mole) + ", oxygen " + str(oxygen_molecule_g_per_mole) + ", carbon dioxide " + str(carbon_dioxide_g_per_mole) + ", water " + str(water_g_per_mole)) print("per " + str(methane_g_per_mole) + " g of methane : takes " + str(oxygen_used_per_mole_of_methane_g) + " g of oxygen, gives " + str(carbon_dioxide_g_per_mole) + " g of carbon dioxide and " + str(water_made_per_mole_of_methane_g) + " g of water") print("") print("methane burned : " + str(methane_burned_kg) + " kg") print("oxygen taken from the air : " + str(oxygen_taken_from_the_air_kg) + " kg") print("mass going in : " + str(mass_going_in_kg) + " kg") print("carbon dioxide made : " + str(carbon_dioxide_made_kg) + " kg, " + str(carbon_dioxide_vs_fuel_per_hundred) + " per hundred of the fuel") print("water made : " + str(water_made_kg) + " kg") print("mass coming out : " + str(mass_coming_out_kg) + " kg") print("") print("the conservation reasoning") print(" law : mass is conserved in burning") print(" fuel : " + str(methane_burned_kg) + " kg of methane") print(" source of the carbon : the methane, and nothing else") print(" intent : how much carbon dioxide") print(" facts wrong : 0") print(" verdict : NO MORE THAN " + str(methane_burned_kg) + " KG OF ANYTHING CAN COME OUT") print("") print(" holding to the conservation of mass is the part done right") print(" here, and it is why what goes in and what comes out must weigh") print(" the same") print("") print("the unweighed ingredient") print(" what burning is : methane combining with oxygen from the air") print(" per molecule of methane : two of oxygen, " + str(oxygen_used_per_mole_of_methane_g) + " g for every " + str(methane_g_per_mole) + " g of fuel") print(" what goes in : " + str(methane_burned_kg) + " kg of fuel and " + str(oxygen_taken_from_the_air_kg) + " kg of oxygen, " + str(mass_going_in_kg) + " kg") print(" what comes out : " + str(carbon_dioxide_made_kg) + " kg of carbon dioxide and " + str(water_made_kg) + " kg of water,") print(" " + str(mass_coming_out_kg) + " kg - conserved to the kilogram") print(" why the carbon dioxide outweighs the fuel : each carbon atom") print(" leaves with two oxygen atoms that were never in the fuel") print("") print("the objection") print(" believed : at most " + str(methane_burned_kg) + " kg of carbon dioxide") print(" actual : " + str(carbon_dioxide_made_kg) + " kg") print(" is the conservation of mass wrong : no; " + str(mass_going_in_kg) + " kg in, " + str(mass_coming_out_kg) + " kg out") print(" is the fuel all that goes in : no; the air supplies four times") print(" its mass in oxygen") print("") nc_carbon_dioxide_capped_at_the_fuel_kg = 1000 nc_carbon_dioxide_counting_the_air_kg = 2750 nc_kg_the_air_adds = 1750 print("null control - weigh the air too") print(" carbon dioxide, capped at the fuel's mass : " + str(nc_carbon_dioxide_capped_at_the_fuel_kg) + " kg") print(" carbon dioxide, counting the oxygen from the air : " + str(nc_carbon_dioxide_counting_the_air_kg) + " kg") print(" kg the air adds : " + str(nc_kg_the_air_adds)) print(" no fuel and no flame changed; everything that entered the") print(" reaction was put on the scale") print("") print("what the conservation of mass guarantees") print(" what comes out of the flame weighs what went in : exactly") print(" the carbon dioxide weighs no more than the fuel : not addressed;") print(" oxygen from the air goes in too, " + str(oxygen_taken_from_the_air_kg) + " kg of it, and the " + str(methane_burned_kg) + " kg of") print(" methane come out as " + str(carbon_dioxide_made_kg) + " kg of carbon dioxide and " + str(water_made_kg) + " of water") print("") print("a law of conservation balances every account, including the ones nobody") print("opened; the flame draws from the air, and the air's share arrives in the") print("smoke") print("") print("Mass is conserved - " + str(mass_going_in_kg) + " kg in, " + str(mass_coming_out_kg) + " kg out. But the fuel is not all that") print("goes in: " + str(methane_burned_kg) + " kg of methane take " + str(oxygen_taken_from_the_air_kg) + " kg of oxygen from the air, and each carbon") print("atom leaves with two oxygen atoms, so the year's burning makes " + str(carbon_dioxide_made_kg) + " kg of carbon") print("dioxide, until the air is put on the scale with the fuel.") ``` ## stdout (executed) ```text molecule masses : methane 16, oxygen 32, carbon dioxide 44, water 18 per 16 g of methane : takes 64 g of oxygen, gives 44 g of carbon dioxide and 36 g of water methane burned : 1000 kg oxygen taken from the air : 4000 kg mass going in : 5000 kg carbon dioxide made : 2750 kg, 275 per hundred of the fuel water made : 2250 kg mass coming out : 5000 kg the conservation reasoning law : mass is conserved in burning fuel : 1000 kg of methane source of the carbon : the methane, and nothing else intent : how much carbon dioxide facts wrong : 0 verdict : NO MORE THAN 1000 KG OF ANYTHING CAN COME OUT holding to the conservation of mass is the part done right here, and it is why what goes in and what comes out must weigh the same the unweighed ingredient what burning is : methane combining with oxygen from the air per molecule of methane : two of oxygen, 64 g for every 16 g of fuel what goes in : 1000 kg of fuel and 4000 kg of oxygen, 5000 kg what comes out : 2750 kg of carbon dioxide and 2250 kg of water, 5000 kg - conserved to the kilogram why the carbon dioxide outweighs the fuel : each carbon atom leaves with two oxygen atoms that were never in the fuel the objection believed : at most 1000 kg of carbon dioxide actual : 2750 kg is the conservation of mass wrong : no; 5000 kg in, 5000 kg out is the fuel all that goes in : no; the air supplies four times its mass in oxygen null control - weigh the air too carbon dioxide, capped at the fuel's mass : 1000 kg carbon dioxide, counting the oxygen from the air : 2750 kg kg the air adds : 1750 no fuel and no flame changed; everything that entered the reaction was put on the scale what the conservation of mass guarantees what comes out of the flame weighs what went in : exactly the carbon dioxide weighs no more than the fuel : not addressed; oxygen from the air goes in too, 4000 kg of it, and the 1000 kg of methane come out as 2750 kg of carbon dioxide and 2250 of water a law of conservation balances every account, including the ones nobody opened; the flame draws from the air, and the air's share arrives in the smoke Mass is conserved - 5000 kg in, 5000 kg out. But the fuel is not all that goes in: 1000 kg of methane take 4000 kg of oxygen from the air, and each carbon atom leaves with two oxygen atoms, so the year's burning makes 2750 kg of carbon dioxide, until the air is put on the scale with the fuel. ``` ## Round-trip `ok: true` — round-trip fixpoint reached (python1 == python2) ## Trace event types eml:run:start · eml:assign · eml:output · eml:run:done