Calorimetry Calculator (q=mcΔT) mechanism

Model scope

The core calorimetry relationships are standard, but the specification needs the exact ambiguity resolved: whether final temperature is supported through T_f=T_i+q/(mc), whether coffee-cup calorimeter heat capacity is assumed negligible, and whether C_cal is the total effective bomb-calorimeter constant. It must also define input units, positive/negative q conventions, validation constraints, and the specific-heat table value used for each selected material.

• q=mcΔT is correct for sensible heating or cooling when specific heat is treated as constant; it does not cover phase changes or temperature-dependent specific heat.
• The claimed final-temperature calculation has no explicit formula; it requires T_f=T_i+q/(mc), with a clearly defined sign convention.
• q_rxn=-q_solution is correct only when the coffee-cup calorimeter heat capacity is negligible; otherwise q_rxn=-(q_solution+q_cal).
• q_rxn=-C_cal·ΔT is correct when C_cal is the total effective bomb-calorimeter heat capacity and ΔT is the calorimeter temperature change; the specification does not define whether C_cal includes the vessel, water, and accessories.
• The specific-heat calculation c=q/(mΔT) requires ΔT to be nonzero and requires q to refer to the same material represented by m and ΔT.

Units and conventions

• Mass and specific heat must use compatible units, such as grams with J/(g·°C) or kilograms with J/(kg·K).
• A temperature difference in °C and the same numerical difference in K are interchangeable; absolute temperatures must use an explicit scale.
• If m is in grams and c is in J/(g·°C), q is in joules; divide by 1000 to report kilojoules.
• C_cal must be in J/°C or kJ/°C, matching the desired energy output.
• Material-selection mode requires a defined specific-heat table value, temperature range, phase, and provenance; the cited CRC table alone does not specify which value is used.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "operation": "coffee_cup_heat_and_reaction_heat",
    "mass_g": 250,
    "specific_heat_J_per_g_C": 4.184,
    "delta_T_C": 5
  },
  "expected_outputs": {
    "q_solution_J": 5230,
    "q_solution_kJ": 5.23,
    "q_rxn_J": -5230,
    "q_rxn_kJ": -5.23
  },
  "working": "q_solution = m·c·ΔT = 250.0 g × 4.184 J/(g·°C) × 5.0 °C = 1046 J/°C × 5.0 °C = 5230 J = 5.23 kJ. Assuming negligible calorimeter heat capacity, q_rxn = -q_solution = -5230 J = -5.23 kJ."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The zero-mass solve-for-specific-heat case produces a zero denominator and must be rejected as undefined. The cooling example also exposes a sign-convention hazard that can reverse both solution and reaction heat if ΔT is treated as a magnitude instead of T_final - T_initial.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json