= Ice-melting calorimetry
<Ice-melting calorimetry> measures the fusion <enthalpy> through <conservation of energy>, rather than inferring it from the small <temperature> change of the <melting> <ice> itself. In a mixing experiment, warm <water> and the container cool while added <ice> melts and the resulting <water> warms. Their combined <energy> balance separates fusion from <sensible heat>.
Weigh the container and stirrer, then weigh the added warm <water> to obtain $m_w$. Let the container and <water> reach a common initial <temperature> $T_i$. Prepare <ice> in a clean <ice>-<water> mixture near $T_m$, rather than assuming freezer <ice> is already at $T_m$; drain and blot its surface immediately before transfer. Add it without splashing, stir gently, and record <temperature> before addition and until after the last <ice> disappears. Reweigh to find the added <mass> $m_i$. Wisconsin's laboratory guide specifies drying each piece, weighing before and after, and recording the <temperature> history; it places the initial and final <temperatures> on opposite sides of the jacket <temperature> to reduce net environmental exchange. https://badger.physics.wisc.edu/trash/lab_old/manual/node30.html[University of Wisconsin, H-2: Latent heat of fusion of ice, procedure]{ref}
For fully melted, initially dry <ice> at $T_m$, a common final <temperature> $T_f>T_m$, constant <water> <specific heat capacity at constant pressure> $c_w$, and apparatus <heat capacity> $C_{\rm cal}$ initially at $T_i$,
$$
(m_wc_w+C_{\rm cal})(T_i-T_f)+Q_{\rm env}=m_iL+m_ic_w(T_f-T_m).
$$
Here $Q_{\rm env}>0$ denotes net <heat> entering the apparatus from its surroundings. The left side supplies the fusion <enthalpy> and the <sensible heat> on the right; the <water> produced by <melting> must be warmed too. The balance extends Case Western's mixing demonstration by including the apparatus and environmental terms. If the <specific heat capacities> vary appreciably, replace their products with the corresponding <temperature> integrals. https://case.edu/artsci/phys/courses/demos/spec.htm[Case Western, mixing-calorimetry energy balance]{ref}
Determine $C_{\rm cal}$ independently, for example by a warm/cold <water> mixing balance with no <phase transition>, including the wetted stirrer and <thermometer> in the apparatus. Check the <thermometer calibration>, keep the lid in place between transfers, and monitor the surroundings. Before/after drift and a comparable run without <ice> help bound $Q_{\rm env}$; such corrections assume comparable <heat transfer> conditions and are not automatically exact. Choosing a jacket <temperature> between $T_i$ and $T_f$ reduces exchange but does not prove $Q_{\rm env}=0$. Ensure all the <ice> has melted and the contents are well mixed before using the measured $T_f$: with residual <ice>, the weighed addition is not the <mass> that has undergone fusion. Repeat the experiment and report <measurement errors> in <mass>, <temperature>, $C_{\rm cal}$ and the leak correction.
An independent way to see the plateau is David Roundy's Oregon State experiment: heat an <ice>-<water> mixture slowly with a waterproof resistor in an insulated cup, stir, and record <temperature>, heater <electric current> $I(t)$, <electric potential difference> $V(t)$ and elapsed time. Plot <temperature> against $E_{\rm el}=\int I(t)V(t)\,dt$, recording changes in $I$ or $V$. The initial <solid> <mass> must exclude accompanying <water>. For a boundary enclosing the heater as well as the sample, this input is electrical <work>, so $\Delta H=E_{\rm el}+Q_{\rm env}$ under the constant-<pressure> assumptions above. Across an ideal isothermal plateau the apparatus has no <sensible heat> change, giving $m_sL=E_{\rm el}+Q_{\rm env}$; departures from uniform <temperature> require accounting for the heater and container response. https://paradigms.physics.oregonstate.edu/act/handout/2108[David Roundy, Oregon State, Ice Calorimetry Lab: apparatus, stirring and electrical input]{ref}
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