Latent Heat of Fusion of Ice lab report

1. Title and aim

Determination of the Latent Heat of Fusion of Ice by the Method of Mixtures. Determine the specific latent heat of fusion of ice (L_f) using the calorimetric method of mixtures, observing the temperature depression resulting from the melting of dried ice chips in warm water inside a calibrated copper calorimeter, and evaluating the thermal energy conservation balance with Rumford radiation compensation.

2. Abstract

Five observations were generated from the ideal teaching model over the settings listed below. A straight-line fit gave an estimate of Latent heat of fusion L_f of 334.13 kJ kg⁻¹, differing by 0.040% from the model value. The reported scatter comes from scale rounding and any stated model approximation, not measured laboratory noise.

3. Apparatus and fixed settings

• Insulated Jacketed Copper Calorimeter with Cork Supports: A thin-walled specularly polished copper container (mass 75.0 g, volume 250 mL) supported on low-conductivity vulcanized cork pegs inside a concentric air jacket, sealed with a wooden lid featuring apertures for the thermometer and stirrer to minimize environmental heat exchange.
• Precision Immersion Calorimetric Thermometer (0.05°C Subdivisions): A sensitive mercury-in-glass thermometer graduated from 10 °C to 45 °C in 0.05 °C divisions, immersed centrally in the water bath to measure the initial warm temperature T_0 and track the cooling descent to the final equilibrium minimum T_f.
• Helical Brass Wire Loop Stirrer: A low-thermal-mass brass wire stirrer formed into an open horizontal loop encircling the thermometer, used to gently circulate the water bath vertically to promote rapid melting and prevent thermal stratification.
• Ice Preparation Dish, Laboratory Tongs, and Absorbent Filter Paper: A clean watch glass holding crushed melting ice chips, paired with laboratory tweezers and sheets of dry lint-free filter paper used to blot each ice fragment completely free of surface water film immediately before immersion.
• Dry melting ice chips at standard thermodynamic equilibrium temperature T_ice = 0.00 °C.
• Initial warm water mass m_w = 200.00 g; initial warm temperature T_0 = 30.00 °C (10.0 °C above ambient room temperature at 20.0 °C).
• Specularly polished copper calorimeter (mass 75.00 g, c_cu = 385.0 J kg⁻¹ K⁻¹); water equivalent W_cal = 28.88 J K⁻¹; C_sys = 866.08 J K⁻¹.
• Specific heat capacity of liquid water c_w = 4186.0 J kg⁻¹ K⁻¹; reference latent heat of fusion of ice L_f = 334.00 kJ kg⁻¹ (334,000 J kg⁻¹ = 79.82 cal g⁻¹).

4. Theory and graph choice

The solid-liquid phase transformation of water at 0 °C is a prototypical first-order thermodynamic transition characterized by a massive latent enthalpy absorption unaccompanied by any temperature variation. In hexagonal ice (ice Ih), water molecules are locked into an open, tetrahedral hydrogen-bonded crystal framework with a low packing density (ρ_ice ≈ 917 kg m⁻³). To break down this rigid lattice into the denser, mobile arrangement of liquid water (ρ_water ≈ 1,000 kg m⁻³), approximately 334 kilojoules of thermal energy must be absorbed per kilogram of ice melted: the specific latent heat of fusion L_f. In quantitative mixture calorimetry, ice chips at their equilibrium melting point (0.00 °C) are introduced into a known mass of warm water held within a calibrated copper calorimeter. As the ice melts, it absorbs latent heat Q_latent = m_i L_f to undergo isothermal phase change, while the resulting meltwater absorbs additional sensible heat Q_melt = m_i c_w (T_f − 0) to warm to the final mixture temperature T_f. Simultaneously, the warm water and calorimeter vessel cool from their initial temperature T_0 to T_f, releasing sensible heat Q_lost = C_sys (T_0 − T_f). Equating thermal loss to thermal gain yields the net latent heat relationship: Q_net = C_sys (T_0 − T_f) − m_i c_w T_f = m_i L_f. By varying the mass of ice added across serial runs and meticulously blotting each ice chip dry with filter paper immediately prior to immersion, ordinary least-squares regression of Q_net against m_i provides an exceptionally clean determination of L_f, while starting the warm water as far above room temperature as the final mixture drops below it eliminates net environmental radiation errors through Rumford compensation.

The calculation fits y = mx + b in SI units. The graph may display scaled axes for readability; those display factors are removed before calculating the physical result. The gradient has units J kg⁻¹.

5. Method

1. Weigh the clean, dry copper calorimeter vessel together with its brass loop stirrer to ±0.01 g on an analytical balance. Add exactly 200.00 g of distilled water warmed to approximately 32 °C. Place the calorimeter inside the protective air jacket and seat the wooden lid firmly.
2. Crush clean, clear ice into small fragments (approximately pea to hazelnut size). Place the ice in a funnel or watch glass and allow it to drain until melting commences freely, establishing a true equilibrium ice-water mixture at 0.00 °C. Spread several dry filter paper sheets nearby.
3. Insert the precision thermometer into the calorimeter water through the lid aperture. Agitate the bath with gentle vertical strokes of the stirrer until the temperature stabilizes. Record the steady initial warm temperature T_0 = 30.00 °C.
4. Take an ice chip with clean tongs, press it firmly between dry filter paper sheets to remove all adhering liquid water film, and drop it immediately into the calorimeter without splashing. Repeat swiftly until the target ice mass (e.g., 15.0 g) has been introduced, closing the lid immediately between additions.
5. Stir the water bath continuously and smoothly with the helical stirrer, watching the thermometer meniscus through an optical magnifier. Track the temperature depression as the ice chips dissolve. Record the lowest stationary temperature attained before environmental re-warming begins as the equilibrium temperature T_f.
6. Remove the calorimeter vessel and reweigh it to ±0.01 g. Determine the exact mass of ice added m_i = m_final − m_initial. Repeat the measurement across five distinct ice charges (15.0 g, 20.0 g, 25.0 g, 30.0 g, and 35.0 g). For each run, compute Q_net = C_sys (T_0 − T_f) − m_i c_w T_f in joules. Plot Q_net against m_i (kg) and evaluate L_f from the slope of the regression line.

6. Observations and calculation table

All observations use fixed model settings. Values are rounded only at the instrument reading stage; further calculations use full precision. Repeated physical trials are not claimed.

Download the sample observations (CSV) ↓

7. Worked calculation for one observation

8. Graph, gradient and final calculation

Dots show the sample observations. The line is the ordinary least-squares fit.

9. Uncertainty and comparison

Percentage difference = |estimate − model value| / |model value| × 100 = 0.0401%. Percentage difference is not experimental uncertainty.

For n = 5 observations, Σresidual² = 44.95379; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 244.82316. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 6.36069.

Propagating only the relevant fit coefficient gives a fit-only standard error of 0.24482 kJ kg⁻¹. This is a one-standard-error quantity under the regression assumptions. Deterministic rounded model data do not supply a complete physical uncertainty budget.

Surface moisture adhering to ice chips (wet ice) introducing pre-melted water that releases zero latent heat, heat exchange with the ambient environment during ice melting and dissolution (~3–5 min), water splashing during ice addition, thermometer thermal lag and stem emergent column correction, spatial thermal stratification before complete agitation, and balance precision in weighing melting ice chips (±0.02 g) contribute experimental uncertainty. The OLS regression standard error reflects random scatter across sample mass settings, but does not capture unmodelled surface water film or residual convection exchanges.

10. Result and discussion

The observations follow the stated model relationship. Check whether the intercept and residual pattern suggest a systematic offset or a missing approximation. Agreement with the model does not independently verify its input constants.

11. Precautions and limitations

• Blot each ice chip thoroughly between dry filter paper sheets immediately before dropping it into the calorimeter to eliminate all adhering liquid moisture.
• Use melting ice chips that are visibly dripping with water at 0 °C rather than sub-zero ice taken directly from a freezer.
• Stir the water bath continuously and gently with the helical stirrer to accelerate dissolution and prevent cold water layers from settling at the bottom.
• Ensure that no water splashes out of the calorimeter when adding ice chips, as splashed water alters both the heat capacity and the final mass.

The teaching simulation models the melting of pure ice under ideal thermal conditions with constant initial warm water temperature T_0 = 30.00 °C, ice temperature T_ice = 0.00 °C, and an invariant system heat capacity C_sys = 866.08 J K⁻¹. In physical experiments, residual surface water film adhering to ice chips can cause negative systematic errors, using freezer ice below 0 °C causes positive errors, water splashing during ice transfer reduces the effective mass, evaporation from the warm surface during dissolution introduces unmodelled cooling, and small departures from symmetric Rumford compensation leave residual radiation exchanges with the room. The simulation evaluates equilibrium temperatures using the exact thermodynamic conservation relation T_f = (C_sys T_0 − m_i L_f) / (C_sys + m_i c_w), where m_i is the dry ice mass in kilograms, L_f = 334,000 J kg⁻¹ (334.00 kJ kg⁻¹) is the reference latent heat of fusion of ice, c_w = 4,186 J kg⁻¹ K⁻¹ is the specific heat capacity of water, T_0 = 30.00 °C is the initial warm water temperature, and C_sys = 866.08 J K⁻¹ is the aggregate thermal capacity. Equilibrium temperatures are rounded to 0.01 °C to simulate precision calorimetric thermometry, and ordinary least-squares regression of Q_net against m_i yields the reported latent heat of fusion.

12. Conclusion

The worked example illustrates how to obtain Latent heat of fusion L_f from measurements, graph variables and a fitted coefficient. The estimate is 334.13 kJ kg⁻¹. A real experiment must additionally evaluate the apparatus-specific uncertainties and corrections described above.