{
    "name": "Calorimetry Heat Transfer Calculator",
    "url": "https://calculators.geekmidst.com/calculators/calorimetry-heat-transfer-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/calorimetry-heat-transfer-calculator.md",
    "category": "Science & engineering",
    "description": "Find the equilibrium temperature when a hot object meets water or another body, and the heat exchanged, with an optional calorimeter heat capacity.",
    "summary": "In an insulated calorimeter, heat lost by the hot body equals heat gained by the cold one. The final temperature is the heat-capacity-weighted average of the starting temperatures.",
    "also_called": [
        "Equilibrium temperature calculator",
        "Mixing temperature calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "m1",
            "label": "Mass of the hot object",
            "type": "number",
            "default": "0.5",
            "unit": "kg"
        },
        {
            "name": "c1",
            "label": "Specific heat of the hot object",
            "type": "number",
            "default": "897",
            "unit": "J/(kg·K)"
        },
        {
            "name": "t1",
            "label": "Starting temperature of the hot object",
            "type": "number",
            "default": "100",
            "unit": "°C"
        },
        {
            "name": "m2",
            "label": "Mass of the water (second body)",
            "type": "number",
            "default": "1",
            "unit": "kg"
        },
        {
            "name": "c2",
            "label": "Specific heat of the water (second body)",
            "type": "number",
            "default": "4184",
            "unit": "J/(kg·K)"
        },
        {
            "name": "t2",
            "label": "Starting temperature of the water (second body)",
            "type": "number",
            "default": "20",
            "unit": "°C"
        },
        {
            "name": "calorimeter",
            "label": "Calorimeter heat capacity",
            "type": "number",
            "default": "",
            "unit": "J/K",
            "optional": true
        }
    ],
    "outputs": [
        {
            "key": "final_temp",
            "label": "Final (equilibrium) temperature",
            "format": "number"
        },
        {
            "key": "heat_kj",
            "label": "Heat transferred from the hot object",
            "format": "number"
        },
        {
            "key": "change_1",
            "label": "Temperature change of the hot object",
            "format": "number"
        },
        {
            "key": "change_2",
            "label": "Temperature change of the water",
            "format": "number"
        }
    ],
    "formula": {
        "text": "T_f = (m₁c₁T₁ + (m₂c₂ + C_cal)T₂) ÷ (m₁c₁ + m₂c₂ + C_cal);  Q = m₁c₁(T₁ − T_f)",
        "variables": {
            "m₁, c₁, T₁": "mass, specific heat and starting temperature of the hot object",
            "m₂, c₂, T₂": "the same for the water or second body",
            "C_cal": "heat capacity of the calorimeter cup"
        }
    },
    "worked_example": {
        "inputs": {
            "m1": "0.5",
            "c1": "897",
            "t1": "100",
            "m2": "1",
            "c2": "4184",
            "t2": "20",
            "calorimeter": ""
        },
        "steps": [
            "m₁c₁ = 0.5 × 897 = 448.5 J/K; m₂c₂ = 1 × 4184 = 4184 J/K.",
            "T_f = (448.5 × 100 + 4184 × 20) ÷ (448.5 + 4184) = 128 530 ÷ 4632.5 = 27.745 °C.",
            "Q = 448.5 × (100 − 27.745) = 32 406 J = 32.41 kJ."
        ],
        "result": "A 0.5 kg block of aluminium at 100 °C dropped into 1 kg of water at 20 °C brings both to about 27.7 °C, transferring 32.4 kJ."
    },
    "interpretation": "Water’s large specific heat means it changes temperature much less than the metal. Measure T_f in the lab and you can solve the same balance backwards for an unknown specific heat.",
    "assumptions": [
        "The system is insulated: no heat is lost to the surroundings.",
        "No phase change or chemical reaction occurs.",
        "Specific heats are constant."
    ],
    "limitations": [
        "If the result is above 100 °C or below 0 °C for water, a phase change would occur and this result is not valid."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "What is the calorimeter constant?",
            "answer": "The heat capacity of the cup, stirrer and thermometer in J/K. It is found by mixing known masses of hot and cold water and is added to the cold side."
        },
        {
            "question": "Why is the heat released positive?",
            "answer": "It is measured from the hot object’s point of view: it loses that much energy, and the water gains the same amount."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Heat Capacity Calculator",
            "url": "https://calculators.geekmidst.com/calculators/heat-capacity-calculator"
        },
        {
            "name": "Temperature Converter",
            "url": "https://calculators.geekmidst.com/calculators/temperature-converter"
        },
        {
            "name": "Thermal Expansion Calculator",
            "url": "https://calculators.geekmidst.com/calculators/thermal-expansion-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}