Determine the specific heat capacity c_s of copper using a water-equivalent jacketed calorimeter and the classical method of mixtures, verifying thermal energy conservation across variable specimen masses, and evaluating radiation heat exchange corrections. Explore a virtual apparatus, collect readings and analyse a graph.
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Readings are generated by an ideal model. The diagram is schematic and is not to scale.
The teaching simulation assumes zero heat transfer during the rapid 1.5-second transit from the steam boiler to the calorimeter, constant specific heats of water and copper over the 20°C to 100°C interval, and instantaneous thermal conduction throughout the specimen pellets. In actual laboratory calorimetry, sensible cooling during transit, radiative and convective heat exchange with room air during the non-isothermal mixing interval, evaporative losses from the agitated warm water surface, and finite thermometer response time constants must be rigorously quantified using Regnault-Pfaundler radiation corrections. The mathematical model integrates a constant calorimeter system thermal capacity C_sys = 920.92 J K⁻¹ (comprising 200.0 g pure water with c_w = 4186.0 J kg⁻¹ K⁻¹ and a 20.0 g water equivalent calorimeter vessel and brass stirrer) and evaluates final equilibrium temperatures using the exact energy balance equation T_f = (m_s c_s T_s + C_sys T_0) / (m_s c_s + C_sys) with pure copper reference specific heat c_s = 385.0 J kg⁻¹ K⁻¹, initial sample temperature T_s = 100.0°C, and initial water temperature T_0 = 20.0°C.
Consists of an inner polished thin-walled copper containment vessel (mass 150.0 g, thermal capacity ~57.8 J K⁻¹), supported on insulating vulcanized cork pegs inside an outer concentric nickel-plated draft-shield jacket with an annular stagnant air gap to suppress convective and conductive heat transfer to the laboratory environment.
A cylindrical brass double-walled steam generator equipped with a vertical central heating chamber, rubber delivery tubing, and a sliding drop bottom shutter, designed to suspend metallic specimens in dry saturated water vapor at 100.0 °C until thermal equilibrium is verified without wetting the sample with condensation.
A paired set of mercury-in-glass standards: one graduated from 0°C to 105°C in 0.5°C divisions for monitoring the steam chamber core temperature, and a high-precision calorimetric thermometer graduated from 15°C to 35°C in 0.05°C subdivisions for detecting slight temperature excursions in the calorimeter.
A low-thermal-capacity looped brass wire stirrer designed to produce rapid convective mixing throughout the 200.0 g water bath without inducing kinetic frictional heating, alongside a two-pan analytical balance resolving mass to ±0.01 g for gravimetric metrology of water and copper specimens.
Determine the specific heat capacity c_s of copper using a water-equivalent jacketed calorimeter and the classical method of mixtures, verifying thermal energy conservation across variable specimen masses, and evaluating radiation heat exchange corrections. Suggested independent settings: 60.0, 100.0, 140.0, 180.0, 220.0 g.
Carefully clean, dry, and weigh the empty inner copper calorimeter vessel together with the dry brass spiral stirrer to ±0.01 g. Record the dry mass m_cal. Multiply m_cal by the specific heat of copper (385 J kg⁻¹ K⁻¹) and the stirrer mass by that of brass (380 J kg⁻¹ K⁻¹), dividing by the specific heat of water (4186 J kg⁻¹ K⁻¹) to establish the theoretical water equivalent W_cal = 0.020 kg (20.0 g). Pipette or dispense exactly 200.0 g of distilled water into the inner vessel, reweigh the filled vessel to confirm m_w = 0.200 kg, mount the vessel on its cork support within the outer insulating jacket, and insert the precision calorimetric thermometer.
Establishing the precise baseline heat capacity of the calorimetric vessel and water bath is critical because all heat transferred from the test specimen distributes across both the liquid water and the metallic containment structures. Any gravimetric error in water mass propagates directly into the inferred system thermal capacity.
Weigh the dry copper specimen pellet charge (selected from 60.0 g to 220.0 g) on the analytical balance to ±0.01 g. Secure the charge inside the perforated copper specimen basket attached to a fine silk suspension thread. Lower the basket into the central heating tube of the Regnault steam generator, plug the top aperture with a loose non-absorbent cotton wool stopper to prevent vertical convective draft losses, and insert the 0–100°C reference thermometer directly into the core of the copper mass. Bring the boiler water to an active, vigorous boil, ensuring steam vents freely through the exhaust port, and soak the specimen until the core thermometer remains perfectly stationary at 100.0 °C for at least five continuous minutes.
Metallic specimens possess finite bulk thermal conductivity, requiring sufficient soaking time for internal temperature gradients to completely decay. Ensuring dry saturated steam conditions guarantees that the specimen surface carries no liquid water droplets into the calorimeter, which would introduce severe latent heat contamination.
Position the jacketed calorimeter assembly adjacent to the steam boiler delivery chute, but shielded by a rigid thermal insulating cardboard screen to prevent radiant heat from the boiler flame reaching the cold calorimeter. Stir the calorimeter water bath gently and continuously with the helical stirrer in steady vertical strokes. Read and record the calorimetric thermometer every 30 seconds for three minutes prior to the transfer to establish the preliminary natural background drift rate ΔT / Δt under ambient laboratory conditions. Confirm that the initial water temperature T_0 is steady at approximately 20.0 °C.
A precise preliminary baseline establishes whether the calorimeter is gaining or losing heat to the ambient room air prior to specimen immersion, which is indispensable for applying Newton's law of cooling radiation corrections to the subsequent temperature rise.
At an agreed timer signal, smoothly swing the calorimeter under the boiler transfer chute or rapidly extract the copper specimen basket by its suspension thread. Immediately lower the glowing hot specimen cleanly into the water of the inner calorimeter vessel, submerging it completely beneath the water surface without touching the thermometer bulb or inner walls, and close the calorimeter lid within one to two seconds. Ensure that no water droplets splash outward from the vessel during entry.
The transfer stage represents the most vulnerable operational window where radiative and convective heat losses to ambient air occur. Minimizing transit duration to under two seconds prevents sensible cooling of the specimen before immersion and eliminates mass loss from splashing.
Commence continuous, smooth vertical agitation using the mechanical brass stirrer at approximately two strokes per second, ensuring intimate liquid circulation around the submerged copper pellets while avoiding surface splashing. Continuously observe the calorimetric thermometer meniscus using a magnifying cathetometer or reading lens to avoid parallax. Record the temperature at 15-second intervals as the mercury column climbs rapidly through an initial transient, peaks at an asymptotic maximum, and begins a very slow subsequent decay. Identify and record the peak equilibrium temperature T_f to ±0.01 °C.
Water has a relatively low thermal conductivity, making mechanical agitation mandatory to break boundary-layer stagnation and achieve isothermal temperature distribution across the bath. Capturing the apex of the cooling curve pinpoints the true state of thermal equilibrium before environmental losses dominate.
Continue recording the calorimeter temperature at one-minute intervals for five minutes following the peak to measure the final cooling rate into the room. Apply the Rumelin or Regnault-Pfaundler radiation correction to adjust T_f for convective and radiative dissipation during the mixing interval. Compute the net thermal energy absorbed by the system Q_sys = C_sys (T_f - T_0) and the thermal mass factor X = m_s (T_s - T_f). Repeat the complete operational sequence for all five specimen masses (60.0, 100.0, 140.0, 180.0, 220.0 g) and perform an ordinary least-squares regression of Q_sys against X to extract the specific heat capacity c_s from the gradient.
Plotting thermal energy absorbed across varied specimen masses linearizes the energy balance equation, averaging out random transfer losses and isolating any constant systematic heat offset as the y-intercept, while the slope yields an unbiased, high-precision estimate of specific heat capacity.
Points are your observations. The fit uses SI x and y values before display scaling.
| # | Specimen mass m_s (g) | Equilibrium temperature T_f (°C) | Heat drop factor m_s (T_s − T_f) (kg K) | Heat absorbed C_sys (T_f − T_0) (J) | Remove |
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