Heat Transfer Calculator

Physics Thermodynamics • Temperature and Zeroth Law

Written by STEM Calculators Team Published January 2, 2026 Updated February 24, 2026

2. Heat Transfer Calculator

Single-material heat transfer with possible phase changes using $Q = mc\Delta T$ (sensible) and $$Q = mL$$ (phase change at constant temperature). Choose an unknown: mass, initial temperature, final temperature, or heat.

Inputs support: pi, e, sqrt(), sin, cos, exp, log. Use * for multiplication. Temperatures are in °C. Convention: $Q>0$ adds heat to the material.

Unknown & inputs

m=1 kg • Ti=−20°C • Tf=15°C

Unknown: Material preset: Thermal model: Mass $m$ (kg): Initial $T_i$ (°C): Final $T_f$ (°C): Heat $Q$ (J):

If the final state lands on a phase plateau ($T_m$ or $T_b$), the tool reports a phase fraction (partial melt/freeze or boil/condense).

Material constants

Enable melt/freeze: Melting/freezing $T_m$ (°C): Latent heat $L_f$ (J/kg): $c_s$ solid (J/kg·K): $c_\ell$ liquid (J/kg·K): Enable boil/condense: Boiling $T_b$ (°C): Latent heat $L_v$ (J/kg): $c_g$ gas (J/kg·K): Single $c$ (J/kg·K):

Animation + plot settings (optional)

Auto-pad (%): Animation speed:

Drag to pan, mouse wheel to zoom, double-click to reset view. Animation uses a dimensionless progress parameter $\tau\in[0,1]$ (not seconds).

Ready

Steps

Enter values and click Solve.

Cooling curve

Temperature $T$ vs specific heat added $q = Q/m$ (plateaus during phase change)

Progress: 0%

Hover to probe $(q,T)$.

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Heat Transfer Calculator — Theory

This calculator models heat transfer for a single material sample using classic heat-transfer formulas: sensible heating/cooling and latent heat during phase changes (constant temperature). We use the sign convention: $$Q>0$$ means heat is added to the sample; $$Q<0$$ means heat is removed.

1) Sensible heat: temperature changes within a phase

\[ Q = mc\Delta T = mc\,(T_f - T_i) \]

$m$: mass (kg)
$c$: specific heat capacity (J/kg·K)
$\Delta T$: temperature change (K or °C difference)

2) Latent heat: phase change at constant temperature

\[ Q = mL \]

During melting/freezing at the melting point $T_m$, the temperature stays constant while energy goes into (or comes out of) the phase transition. The same idea applies at the boiling point $T_b$ for boiling/condensing.

$L_f$: latent heat of fusion (J/kg)
$L_v$: latent heat of vaporization (J/kg)

3) Stage method (the key idea)

Real problems often cross phase points. Instead of using one formula, we split the process into stages:

Heat/cool within a phase using $Q=mc\Delta T$.
If you reach $T_m$, you may need a melting/freezing stage using $Q=mL_f$ (possibly partial).
If you reach $T_b$, you may need a boiling/condensing stage using $Q=mL_v$ (possibly partial).
Continue with sensible heat in the new phase if heat remains.

4) Solving different unknowns

A) Unknown heat $Q$

\[ Q = \sum_k Q_k \]

Sum sensible and latent stages from $T_i$ to $T_f$.

B) Unknown mass $m$

\[ Q = m\,q(T_i\to T_f)\quad\Rightarrow\quad m = \frac{Q}{q(T_i\to T_f)} \]

Here $q(T_i\to T_f)$ is the heat per kilogram needed for the stage method from $T_i$ to $T_f$.

C) Unknown final temperature $T_f$

Apply the known heat $Q$ to the initial state and walk along the stages until the energy is exhausted. If you run out of heat during a latent stage, the final temperature equals the phase point and the tool reports a phase fraction.

D) Unknown initial temperature $T_i$

Use reversibility of the stage method: starting from $T_f$, applying heat $-Q$ takes you back to $T_i$.

5) Example (ice + heating to water)

Suppose water starts as ice at $-20^\circ\mathrm{C}$ and ends as liquid water at $15^\circ\mathrm{C}$. The stages are:

\[ Q = m c_s (0 - (-20)) \;+\; mL_f \;+\; m c_\ell (15 - 0) \]

The temperature remains at $0^\circ\mathrm{C}$ during melting while latent heat is absorbed.

Notes

Preset constants are typical values (often near 1 atm). Real values depend on pressure and purity.
If you disable phase changes, the model reduces to $Q=mc\Delta T$ only.
The graph shows $T$ vs $q=Q/m$. Flat segments indicate phase-change plateaus.

Steps

Cooling curve

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