{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"mixing-temperature"},"result":{"entity_type":"calculator","id":"mixing-temperature","calculator_id":"mixing-temperature","canonical_url":"https://tttkmbb.com/physics/mixing-temperature","name":"Mixing Temperature Calculator","title":"Mixing Temperature Calculator – Final Temperature of Two or Three Mixed Bodies (Calorimetry)","category":"physics","category_name":"Physics","tool_name":"calculate_mixing_temperature","featured_mcp_tool":false,"description":"Computes the equilibrium temperature reached when two or three bodies of known mass, specific heat and initial temperature exchange heat, from energy conservation Σ m·c·(T − T_final) = 0, and the heat that flows from the hotter to the cooler bodies.","use_when":"You mix hot and cold water, drop a heated metal into a liquid, or combine up to three substances and need the final common temperature or the heat exchanged (calorimetry without phase change).","do_not_use_when":"A substance melts, boils or freezes during the exchange (latent heat is not included), the container or surroundings absorb significant heat, or you only need the heat for a given temperature change of one body (use specific-heat).","inputs":[{"name":"mass_1_kg","label":"Mass of body 1","type":"number","unit":"kg","required":true,"exclusive_min":0,"description":"Mass of the first body in kilograms (1 L of water ≈ 1 kg).","example":1},{"name":"specific_heat_1_j_kg_k","label":"Specific heat of body 1","type":"number","unit":"J/(kg·K)","required":false,"default":4186,"max":100000,"exclusive_min":0,"description":"Specific heat capacity of body 1: water 4186, ice 2090, aluminium 897, iron 449, copper 385, ethanol 2440.","example":4186},{"name":"temperature_1_c","label":"Initial temperature of body 1","type":"number","unit":"°C","required":true,"min":-273.15,"max":5000,"description":"Initial temperature of body 1 in °C.","example":80},{"name":"mass_2_kg","label":"Mass of body 2","type":"number","unit":"kg","required":true,"exclusive_min":0,"description":"Mass of the second body in kilograms.","example":2},{"name":"specific_heat_2_j_kg_k","label":"Specific heat of body 2","type":"number","unit":"J/(kg·K)","required":false,"default":4186,"max":100000,"exclusive_min":0,"description":"Specific heat capacity of body 2 (default: liquid water, 4186).","example":4186},{"name":"temperature_2_c","label":"Initial temperature of body 2","type":"number","unit":"°C","required":true,"min":-273.15,"max":5000,"description":"Initial temperature of body 2 in °C.","example":20},{"name":"mass_3_kg","label":"Mass of body 3 (optional)","type":"number","unit":"kg","required":false,"default":0,"min":0,"description":"Mass of an optional third body in kilograms; leave at 0 for a two-body mixture.","example":0.5},{"name":"specific_heat_3_j_kg_k","label":"Specific heat of body 3","type":"number","unit":"J/(kg·K)","required":false,"default":4186,"max":100000,"exclusive_min":0,"description":"Specific heat capacity of body 3 (default: liquid water, 4186).","example":4186},{"name":"temperature_3_c","label":"Initial temperature of body 3","type":"number","unit":"°C","required":false,"min":-273.15,"max":5000,"description":"Initial temperature of body 3 in °C; required when mass_3_kg is greater than 0.","example":50}],"outputs":[{"name":"final_temperature_c","label":"Final temperature","type":"number","unit":"°C","decimals":2,"description":"Common equilibrium temperature T_final = Σ m·c·T / Σ m·c."},{"name":"final_temperature_f","label":"Final temperature","type":"number","unit":"°F","decimals":2,"description":"Equilibrium temperature in degrees Fahrenheit."},{"name":"final_temperature_k","label":"Final temperature","type":"number","unit":"K","decimals":2,"description":"Equilibrium temperature in kelvin."},{"name":"heat_transferred_j","label":"Heat transferred","type":"number","unit":"J","decimals":2,"description":"Heat given up by the bodies hotter than T_final (equal to the heat absorbed by the cooler ones); for two bodies m1·c1·|T1 − T_final|."},{"name":"heat_transferred_kj","label":"Heat transferred","type":"number","unit":"kJ","decimals":4,"description":"Heat transferred in kilojoules."},{"name":"note","label":"Note","type":"string","decimals":4,"description":"Which bodies cool and which warm, and the assumptions (constant specific heats, no phase change, no losses)."}],"input_schema":{"type":"object","properties":{"mass_1_kg":{"description":"Mass of the first body in kilograms (1 L of water ≈ 1 kg). Unit: kg.","type":"number","exclusiveMinimum":0,"examples":[1],"x-unit":"kg"},"specific_heat_1_j_kg_k":{"description":"Specific heat capacity of body 1: water 4186, ice 2090, aluminium 897, iron 449, copper 385, ethanol 2440. Unit: J/(kg·K).","type":"number","maximum":100000,"exclusiveMinimum":0,"default":4186,"examples":[4186],"x-unit":"J/(kg·K)"},"temperature_1_c":{"description":"Initial temperature of body 1 in °C. Unit: °C.","type":"number","minimum":-273.15,"maximum":5000,"examples":[80],"x-unit":"°C"},"mass_2_kg":{"description":"Mass of the second body in kilograms. Unit: kg.","type":"number","exclusiveMinimum":0,"examples":[2],"x-unit":"kg"},"specific_heat_2_j_kg_k":{"description":"Specific heat capacity of body 2 (default: liquid water, 4186). Unit: J/(kg·K).","type":"number","maximum":100000,"exclusiveMinimum":0,"default":4186,"examples":[4186],"x-unit":"J/(kg·K)"},"temperature_2_c":{"description":"Initial temperature of body 2 in °C. Unit: °C.","type":"number","minimum":-273.15,"maximum":5000,"examples":[20],"x-unit":"°C"},"mass_3_kg":{"description":"Mass of an optional third body in kilograms; leave at 0 for a two-body mixture. Unit: kg.","type":"number","minimum":0,"default":0,"examples":[0.5],"x-unit":"kg"},"specific_heat_3_j_kg_k":{"description":"Specific heat capacity of body 3 (default: liquid water, 4186). Unit: J/(kg·K).","type":"number","maximum":100000,"exclusiveMinimum":0,"default":4186,"examples":[4186],"x-unit":"J/(kg·K)"},"temperature_3_c":{"description":"Initial temperature of body 3 in °C; required when mass_3_kg is greater than 0. Unit: °C.","type":"number","minimum":-273.15,"maximum":5000,"examples":[50],"x-unit":"°C"}},"additionalProperties":false,"required":["mass_1_kg","temperature_1_c","mass_2_kg","temperature_2_c"]},"output_schema":{"type":"object","properties":{"final_temperature_c":{"description":"Common equilibrium temperature T_final = Σ m·c·T / Σ m·c. Unit: °C.","type":"number","x-unit":"°C"},"final_temperature_f":{"description":"Equilibrium temperature in degrees Fahrenheit. Unit: °F.","type":"number","x-unit":"°F"},"final_temperature_k":{"description":"Equilibrium temperature in kelvin. Unit: K.","type":"number","x-unit":"K"},"heat_transferred_j":{"description":"Heat given up by the bodies hotter than T_final (equal to the heat absorbed by the cooler ones); for two bodies m1·c1·|T1 − T_final|. Unit: J.","type":"number","x-unit":"J"},"heat_transferred_kj":{"description":"Heat transferred in kilojoules. Unit: kJ.","type":"number","x-unit":"kJ"},"note":{"description":"Which bodies cool and which warm, and the assumptions (constant specific heats, no phase change, no losses).","type":"string"}}},"formula":"final_temperature_c = (m1·c1·T1 + m2·c2·T2 + m3·c3·T3) / (m1·c1 + m2·c2 + m3·c3); heat_transferred_j = Σ over bodies with T_i > T_final of m_i·c_i·(T_i − T_final) (= m1·c1·|T1 − T_final| for two bodies); °F = °C × 9/5 + 32; K = °C + 273.15","method":"Energy conservation in an ideal calorimeter: heat lost by the hotter bodies equals heat gained by the cooler ones, with constant specific heats, no phase change and no heat exchange with the container or surroundings.","sources":[{"name":"Wikipedia – Calorimetry","url":"https://en.wikipedia.org/wiki/Calorimetry","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Specific heat capacity","url":"https://en.wikipedia.org/wiki/Specific_heat_capacity","type":"reference","retrieved_at":"2026-09-24"},{"name":"HyperPhysics – Specific heat","url":"http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/spht.html","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"1 kg water at 80 °C + 2 kg water at 20 °C","inputs":{"mass_1_kg":1,"temperature_1_c":80,"mass_2_kg":2,"temperature_2_c":20},"expected":{"final_temperature_c":40,"final_temperature_f":104,"final_temperature_k":313.15,"heat_transferred_j":167440,"heat_transferred_kj":167.44},"url":"https://tttkmbb.com/api/v1/calculate/mixing-temperature?mass_1_kg=1&temperature_1_c=80&mass_2_kg=2&temperature_2_c=20"},{"name":"0.5 kg copper (385 J/kg·K) at 100 °C into 1 kg water at 20 °C","inputs":{"mass_1_kg":0.5,"specific_heat_1_j_kg_k":385,"temperature_1_c":100,"mass_2_kg":1,"temperature_2_c":20},"expected":{"final_temperature_c":23.52,"heat_transferred_j":14722.94,"heat_transferred_kj":14.7229},"url":"https://tttkmbb.com/api/v1/calculate/mixing-temperature?mass_1_kg=0.5&specific_heat_1_j_kg_k=385&temperature_1_c=100&mass_2_kg=1&temperature_2_c=20"}],"faq":[{"q":"Why is the final temperature of copper in water so close to the water temperature?","a":"Water's specific heat (4186 J/kg·K) is about 11 times copper's (385), so 1 kg of water has far more heat capacity than 0.5 kg of copper and its temperature barely moves."},{"q":"Can I mix ice and water with this calculator?","a":"Only if no ice melts. Melting takes 334 kJ/kg of latent heat that this calculator ignores, so for ice-water mixtures the real final temperature is lower than the result."},{"q":"Does the container matter?","a":"A real container absorbs some heat. Enter it as body 3 (mass × specific heat of the vessel, at the initial temperature of its contents) to include it."}],"tags":["mixing temperature","final temperature","calorimetry","heat transfer","thermal equilibrium","mixing hot and cold water"],"related":[{"calculator_id":"specific-heat","reason":"Heat for a given temperature change of a single body (Q = m·c·ΔT)."},{"calculator_id":"temperature","reason":"Convert temperatures between °C, °F and K."},{"calculator_id":"thermal-expansion","reason":"Size change of a solid caused by the temperature change."}],"links":{"html":"https://tttkmbb.com/physics/mixing-temperature","markdown":"https://tttkmbb.com/physics/mixing-temperature.md","json":"https://tttkmbb.com/physics/mixing-temperature.json","api":"https://tttkmbb.com/api/v1/calculate/mixing-temperature","schema":"https://tttkmbb.com/api/v1/calculators/mixing-temperature","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:45:46Z","next_actions":[{"tool":"run_calculator","calculator_id":"mixing-temperature","reason":"Run Mixing Temperature Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/physics/mixing-temperature.md"}}