All calculatorsCalorimetry Calculator
Solve calorimetry problems using q = m·c·ΔT, mixing (final temperature), phase change (q = m·L), and a heating curve (melting/boiling segments). Includes unit conversions, quick picks, optional steps, and a mini visual.
Background
Calorimetry tracks heat transfer. For temperature changes: q = m·c·ΔT. For phase changes: q = m·L. In mixing problems, energy is conserved: heat lost by hot equals heat gained by cold (plus any calorimeter heat, if included).
How to use this calculator
- Pick a problem type at the top: q = m·c·ΔT, Mixing, Phase change, or Heating curve.
- Choose your sign convention (optional). q > 0 can mean the system gains heat (common in chemistry), or the surroundings gain heat. The calculator computes internally using the system convention and flips the displayed sign if you choose “surroundings.”
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Enter the values you know.
- In Temperature change mode, use “Solve for” to pick what you want (q, m, c, or ΔT), then fill in the other fields and leave the target blank (or ignore it).
- In Mixing mode, enter hot + cold masses and temperatures. Add C_cal only if your problem gives it. (Most intro problems ignore it.)
- In Phase change mode, enter mass and latent heat (or use a preset) to solve q = m·L.
- In Heating curve mode, enter m, T_i, and T_f (or enter q to solve for T_f). The calculator automatically adds the relevant segments (warming + melting/boiling if crossed).
- Use Quick picks if you want a ready-made example. Clicking a chip fills the form and runs the calculation.
- Click Calculate (or leave Auto-calculate on). Turn on Show step-by-step to see the setup and algebra, and Show mini visual to get a quick heat-flow / heating-curve style visual.
Common gotchas: (1) Use grams when your c is in J/(g·°C). (2) ΔT is the same size in °C and K. (3) In mixing problems, T_f must land between T_hot and T_cold if there’s no phase change and the system is insulated.
How this calculator works
- Temperature change: rearranges q = m·c·ΔT to solve for the missing value.
- Mixing: solves energy balance: m_h c_h (T_h − T_f) = m_c c_c (T_f − T_c) (+ C_cal(T_f − T_c) if enabled).
- Phase change: uses q = m·L and converts units as needed.
- Heating curve: sums sensible-heat segments plus latent heats at melting/boiling: q_total = Σ(m·c·ΔT) + m·L_f + m·L_v (as applicable).
Reminder: ΔT is the same size in °C and K. Only absolute temperatures differ.
Formula & Equation Used
Temperature change: q = m·c·ΔT
Mixing (no cup): m_h c_h (T_h − T_f) = m_c c_c (T_f − T_c)
Mixing (with cup): m_h c_h (T_h − T_f) = m_c c_c (T_f − T_c) + C_cal (T_f − T_c)
Phase change: q = m·L
Heating curve segments:
q_1 = m·c_s·(T_m − T_i) (warm solid to melting point)
q_2 = m·L_f (melt at T_m)
q_3 = m·c_l·(T_b − T_m) (warm liquid to boiling point)
q_4 = m·L_v (boil at T_b)
q_5 = m·c_g·(T_f − T_b) (warm vapor above boiling point)
Not every problem includes all segments — the calculator only applies the segments you cross from T_i to T_f.
Example Problems & Step-by-Step Solutions
Example 1 — Heating water
100 g of water warms from 20°C to 35°C. Find q.
- ΔT = 35 − 20 = 15°C
- q = m·c·ΔT = (100)(4.184)(15) = 6276 J ≈ 6.28 kJ
Example 2 — Mixing hot metal into water (conceptual)
Energy lost by hot object = energy gained by cold object (and the cup if needed). Use m_h c_h (T_h − T_f) = m_c c_c (T_f − T_c), then solve for T_f.
Example 3 — Melting ice
Melt 25 g ice at 0°C. Find q using L_f ≈ 334 J/g.
- q = m·L = (25)(334) = 8350 J
Example 4 — Heating curve (water, simplified)
Heat 50 g of ice from −10°C to 120°C at ~1 atm. Find total q (use water values).
- Warm ice: q_1 = m·c_s·ΔT (−10→0°C)
- Melt: q_2 = m·L_f
- Warm water: q_3 = m·c_l·ΔT (0→100°C)
- Boil: q_4 = m·L_v
- Warm steam: q_5 = m·c_g·ΔT (100→120°C)
The calculator performs this automatically and reports each segment if “Show step-by-step” is enabled.
Frequently Asked Questions
Q: Is ΔT different in °C vs K?
No. A temperature change of 10°C equals a change of 10 K.
Q: When do I use C_cal?
Use it when the problem gives a calorimeter constant (or asks you to account for the cup/thermometer heat).
Q: Why is heat “lost” sometimes negative?
It’s a sign convention. Many setups use q < 0 for the hot object (it cools) and q > 0 for the cold object (it warms). This calculator lets you choose the display convention.
Q: Does the heating curve assume 1 atm?
Yes — it uses melting/boiling points and latent heats as if the phase changes occur at ~1 atm (typical gen-chem assumption).
