Thermal properties of matter

What you will understand

For NEET UG Physics students: separate heat from temperature, split warming and phase changes into energy stages, and test whether all the ice can melt before solving for a final temperature.

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Quick answer: identify the phase before the formula

Heat is energy transferred because of a temperature difference; temperature is a state variable, not an amount of stored heat. Within one phase over a range where specific heat c is approximately constant, use $Q=mc\Delta T$. During a phase transition of a pure substance at its transition temperature and fixed pressure, use $Q=mL$ for the mass changing phase. Its temperature can stay constant while energy enters. A body has internal energy; it does not possess a state-function “heat content”.

See where each part of the supplied energy goes

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A calorimetry equation needs a possible final state

For an insulated mixing model with negligible container heat capacity, no evaporation and no other energy input, balance heat lost against heat gained. Before assuming the final mixture is all liquid above zero, compare the heat that warm water can release on cooling to zero with the heat required to melt all the ice at zero. If insufficient, the equilibrium mixture still contains ice at zero under the stated pure-water pressure model. Do not continue an all-liquid equation to an impossible negative temperature while liquid water and ice coexist in this example.

Compare two melting tests before finding a final temperature

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Temperature differences and free expansion need different checks

A temperature difference of 10 Celsius degrees is 10 K, so a temperature-change calculation does not add 273.15 to $\Delta T$. Absolute-temperature ratios and radiation formulas require kelvin. For a freely expanding isotropic solid with small changes and a supplied constant linear coefficient, $\Delta L\simeq\alpha L_0\Delta T$. With $L_0=1.00\,\mathrm m$, $\alpha=2.0\times10^{-5}\,\mathrm{K^{-1}}$ and $\Delta T=50\,\mathrm K$, extension is $0.0010\,\mathrm m=1.0\,\mathrm{mm}$. Restraining expansion can introduce stress; the free-expansion formula alone does not solve that different setup.

Heat amount is different from heat-transfer rate

Specific heat c has unit $\mathrm{J\,kg^{-1}\,K^{-1}}$; a sample’s heat capacity C is $mc$ with unit $\mathrm{J/K}$. Latent heat L has unit $\mathrm{J/kg}$. Thermal conductivity has unit $\mathrm{W\,m^{-1}\,K^{-1}}$ and belongs to a heat-flow-rate model, not a phase-change energy. A supplied heater power P gives transferred energy $Q=Pt$ only when the specified power actually reaches the sample over time t; account for losses or inefficiency if given.

Common mistakes: name what the energy changes

Do not average temperatures without accounting for masses, heat capacities and phase changes. Do not add 273.15 to a temperature difference. A zero temperature change does not prove zero transferred heat during melting or boiling. Check whether all the ice melts before using the total liquid mass in a final-temperature equation. The approximate constants and pressure conditions in these examples define the model; melting/boiling temperatures and heat capacities are not universal constants independent of conditions.

Try it: melting without a temperature rise

Supply $10.0\,\mathrm{kJ}$ to $0.10\,\mathrm{kg}$ pure ice already at $0\,{}^\circ\mathrm C$ near one atmosphere, with no losses. Use $L_f=334000\,\mathrm{J/kg}$. Does the sample become warmer liquid water?

Try it: equal specific heat does not mean equal mass

Mix $0.10\,\mathrm{kg}$ liquid water at $80\,{}^\circ\mathrm C$ with $0.30\,\mathrm{kg}$ water at $20\,{}^\circ\mathrm C$. No phase change occurs. Neglect heat loss and cup heat capacity; use equal constant specific heats. Is the final temperature 50 Celsius?

Come back tomorrow: choose the phase before substituting

Explain why melting can absorb heat without a temperature rise. Then predict whether a new mixture has enough energy to melt all its ice before calculating a final temperature. Use the diagram only after making that prediction.

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Sources and review

Technical review: Codex (automated). Primary textbook sources checked on 23 October 2026. Diagrams, worked examples and self-checks are original. Supplied property values define simplified teaching models; no measured dataset or human subject review is claimed.