Latent Heat of Vaporization lab report

1. Title and aim

Determination of the Latent Heat of Vaporization of Water by Condensation Calorimetry. Determine the specific latent heat of vaporization of water (L_v) by condensing dry steam into a known mass of cold water inside a calibrated copper calorimeter, measuring the resulting temperature elevation, and analyzing the thermal energy balance with radiation exchange corrections.

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 vaporization L_v of 2260.36 kJ kg⁻¹, differing by 0.016% 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

• Copper Steam Generator Boiler with Safety Manometer and Burner: A robust cylindrical copper boiler equipped with a water-level sight glass, a vertical safety pressure-release manometer tube, and an adjustable Bunsen burner to produce a steady, vigorous stream of saturated steam at 100.0 °C.
• Glass Condensate Water Trap (Steam Dryer): An inline bulbous glass trap inserted between the boiler and delivery tube to catch, collect, and drain entrained liquid water droplets, guaranteeing that only dry saturated vapor reaches the calorimeter vessel.
• Polished Copper Calorimeter in Water-Jacketed Enclosure with Insulated Lid: A thin-walled cylindrical copper container (mass 75.0 g) supported on insulating cork pegs inside a concentric air jacket, sealed with a vulcanite lid with apertures for the steam delivery tube, thermometer, and stirrer.
• Precision Calorimetric Thermometer and Analytical Balance: A high-resolution mercury-in-glass thermometer graduated from 10 °C to 50 °C in 0.05 °C divisions to measure T_0 and T_f, paired with a dual-pan analytical balance resolving mass to ±0.01 g to determine the condensed steam mass m_v.
• Steam boiler temperature T_s = 100.00 °C (under standard barometric pressure of 760 mmHg).
• Initial cold water mass m_w = 200.00 g; initial chilled temperature T_0 = 15.00 °C (compensating for 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.
• Reference latent heat of vaporization of water: L_v = 2260.00 kJ kg⁻¹ (2,260,000 J kg⁻¹ = 539.8 cal g⁻¹).

4. Theory and graph choice

Vaporization represents one of the most energetic first-order phase transformations in classical thermodynamics. When liquid water at its boiling point transforms into saturated water vapor, an immense quantity of thermal energy—the specific latent heat of vaporization L_v—must be supplied to overcome the robust intermolecular hydrogen-bonding network and to perform mechanical expansion work against the surrounding atmospheric pressure as the specific volume increases by a factor of over 1,600. Conversely, when dry saturated steam condenses inside a cooler aqueous medium, it releases this identical quantity of latent enthalpy alongside the sensible heat of the condensed liquid as it cools from the boiling temperature T_s to the final mixture temperature T_f. In quantitative condensation calorimetry, dry steam generated in a dedicated boiler is conducted through a glass water trap designed to intercept entrained liquid droplets, ensuring that only pure gaseous phase enters the calorimeter. The thermal energy absorbed by the cold water bath, the thin-walled copper calorimeter vessel, and its stirrer equals the total heat liberated by the condensing steam: C_sys (T_f − T_0) = m_v L_v + m_v c_w (T_s − T_f). Rearranging this fundamental conservation equation isolates the net latent heat transfer: Q_net = C_sys (T_f − T_0) − m_v c_w (T_s − T_f) = m_v L_v. By executing condensation trials across varying charges of condensed steam, ordinary least-squares regression of Q_net against m_v yields a highly accurate evaluation of L_v, while the implementation of Count Rumford's radiation compensation technique—initiating trials as far below ambient room temperature as the final mixture rises above it—effectively eliminates net environmental radiation bias.

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 wire loop stirrer to ±0.01 g. Add exactly 200.00 g of distilled water pre-cooled to approximately 14 °C to 15 °C (approximately 5 °C below room temperature, T_room = 20.0 °C). Place the calorimeter vessel inside the double-walled outer jacket and seat the insulated lid firmly.
2. Fill the copper boiler two-thirds full with distilled water, add anti-bumping boiling chips, and heat vigorously with the Bunsen burner. Connect the delivery tube through the glass water trap. Allow steam to blast freely through the trap into a waste beaker for at least three minutes until the trap and delivery nozzle are thoroughly pre-heated and discharging clean, dry steam without sputtering.
3. Agitate the calorimeter water bath gently with the wire stirrer and record the steady initial temperature T_0 = 15.00 °C. Position the calorimeter beneath the pre-heated steam delivery nozzle, lower the nozzle tip approximately 2 cm below the water surface, and allow steam to bubble into the liquid while maintaining continuous, gentle stirring.
4. Monitor the rising temperature closely. When the water temperature approaches approximately 25 °C to 35 °C (so the final temperature excess above room temperature roughly mirrors the initial depression below room temperature), pinch the rubber delivery hose, remove the delivery nozzle promptly from the water, and shake any adhering droplets back into the calorimeter.
5. Continue stirring the water bath thoroughly until the thermometer reaches its maximum steady reading, recording this value as the final equilibrium temperature T_f. Remove the calorimeter vessel from its jacket and reweigh it to ±0.01 g. Subtract the initial tare mass to determine the exact mass of condensed steam m_v = m_final − m_initial.
6. Repeat the condensation procedure across five distinct steam charges (m_v = 3.0 g, 4.5 g, 6.0 g, 7.5 g, and 9.0 g). For each run, compute the sensible heat absorbed by the system Q_gain = C_sys (T_f − T_0) and subtract the sensible heat lost by the condensed water cooling from 100 °C to T_f: Q_sens = m_v c_w (T_s − T_f). Plot Q_net = Q_gain − Q_sens against m_v (kg) and extract the latent heat of vaporization L_v from the slope.

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 = 0.0158%. Percentage difference is not experimental uncertainty.

For n = 5 observations, Σresidual² = 0.77850; s² = Σresidual²/(n − 2). Gradient standard error = √[s²/Σ(x − x̄)²] = 107.39357. Intercept standard error = √[s²(1/n + x̄²/Σ(x − x̄)²)] = 0.68345.

Propagating only the relevant fit coefficient gives a fit-only standard error of 0.10739 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.

Water droplet carryover (wet steam) passing through the delivery tube despite the steam trap, radiation and convective heat exchanges during the condensation interval (~5–10 min), evaporation loss from the agitated warm water surface, thermometer stem emergent column cooling, atmospheric barometric pressure departure altering steam boiling temperature Ts from 100.0°C (±0.037°C per mmHg), and analytical balance precision in measuring condensed steam mass (±0.01 g) contribute experimental uncertainty. The OLS regression standard error reflects random scatter across condensation charges, but does not capture unmodelled entrained moisture or residual radiation offsets.

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

• Blast steam vigorously through the water trap into a waste beaker for several minutes to thoroughly pre-heat the glass delivery tube before inserting it into the calorimeter.
• Wipe the exterior of the delivery nozzle immediately before immersion and withdraw it promptly when heating ceases to avoid back-siphoning.
• Stir the calorimeter water continuously and gently to ensure rapid mixing and complete thermal equilibration without splashing.
• Reweigh the calorimeter immediately after the run with its lid on to prevent evaporative loss from corrupting the condensed steam mass measurement.

The teaching simulation models condensation calorimetry under ideal dry steam conditions with constant steam temperature T_s = 100.00 °C, initial water temperature T_0 = 15.00 °C, and an invariant system heat capacity C_sys = 866.08 J K⁻¹. In physical laboratory execution, entrained liquid water droplets escaping through the steam trap can introduce wet steam errors, evaporative cooling from the warm water surface can reduce the apparent equilibrium temperature, thermometer stem emergent exposure can slightly depress readings, and barometric pressure departures alter the true boiling point from 100 °C. The simulation evaluates equilibrium temperatures using the exact thermodynamic conservation relation T_f = (m_v L_v + m_v c_w T_s + C_sys T_0) / (C_sys + m_v c_w), where m_v is the condensed steam mass in kilograms, L_v = 2,260,000 J kg⁻¹ (2,260.00 kJ kg⁻¹) is the reference latent heat of vaporization, c_w = 4,186 J kg⁻¹ K⁻¹ is the specific heat capacity of water, T_s = 100.00 °C is the steam temperature, T_0 = 15.00 °C is the initial chilled 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_v yields the reported latent heat of vaporization.

12. Conclusion

The worked example illustrates how to obtain Latent heat of vaporization L_v from measurements, graph variables and a fitted coefficient. The estimate is 2260.36 kJ kg⁻¹. A real experiment must additionally evaluate the apparatus-specific uncertainties and corrections described above.