To investigate the variation of electrical resistance of a metallic copper conductor as a function of temperature, determine its temperature coefficient of resistance (α) and reference resistance at 0 °C (R₀) via linear regression, and extrapolate the inferred absolute zero of resistance. Explore a virtual apparatus, collect readings and analyse a graph.
Ready for a virtual observation.
Adjust the apparatus, then take a reading.
Timing is generated from the model; a short on-screen trial represents a longer physical interval. Animation is illustrative.
Calculations assume uniform thermal equilibrium between the bath and copper winding, negligible Joule self-heating (excitation current ≤ 1 mA), and neglect higher-order quadratic Callendar-Van Dusen curvature which contributes < 0.05% below 100 °C. Real copper specimens exhibit slight residual resistance at cryogenic temperatures (Matthiessen's rule: ρ = ρ_residual + ρ_phonon(T)), while industrial platinum RTDs incorporate small second-order coefficients (B ≈ −5.775 × 10⁻⁷ °C⁻²).
Provides a non-inductively wound bifilar coil of high-purity electrolytic copper wire (calibrated nominal resistance R₀ = 100.00 Ω at 0.0 °C) sealed inside a thin-walled protective brass sheath for rapid thermal equilibrium.
Provides a thermally insulated fluid bath fitted with electric immersion heating elements, an ice-water cooling stage, and continuous mechanical stirring to maintain stable and uniform temperature from 0.0 °C to 100.0 °C.
Measures bath temperature from −5.0 °C to +105.0 °C with 0.1 °C resolution, immersed alongside the copper coil sheath to track true equilibrium fluid temperature.
Measures coil resistance with 0.01 Ω resolution using a Kelvin 4-wire sensing configuration (independent source current and sense voltage leads) to eliminate lead and contact resistances.
Prevents thermal stratification, convective fluid layering, and localized temperature gradients between the heating elements, thermometer bulb, and resistance coil sheath.
Supports the thermometer and coil assembly securely at the geometric center of the bath while minimizing evaporative heat losses and thermal drafts from the laboratory.
To investigate the variation of electrical resistance of a metallic copper conductor as a function of temperature, determine its temperature coefficient of resistance (α) and reference resistance at 0 °C (R₀) via linear regression, and extrapolate the inferred absolute zero of resistance. Suggested independent settings: 0.0, 20.0, 40.0, 60.0, 80.0, 100.0 °C.
Immerse the copper coil sheath and calibrated mercury thermometer into a vigorously stirred equilibrium mixture of crushed distilled ice and pure water at 0.0 °C. Connect the four terminals of the digital bridge (two current leads, two potential leads) to the coil binding posts. Wait 5 minutes for complete thermal equilibrium and record the ice-point baseline resistance R₀ = 100.00 Ω.
Measuring the exact ice-point resistance R₀ at 0.0 °C establishes the true zero-intercept baseline required to calculate the temperature coefficient α = m / R₀.
Transfer the coil and thermometer into the thermostatically controlled heating bath filled with distilled water. Activate the motorized circulation stirrer at moderate speed to ensure vigorous convective fluid mixing throughout the tank, eliminating vertical temperature stratification.
Continuous circulation guarantees that the mercury thermometer bulb and the copper coil winding experience the exact same fluid temperature.
Energize the immersion heater to elevate the bath temperature to approximately 20.0 °C. Throttle the heater power and monitor the thermometer until the temperature stabilizes to within ±0.1 °C for at least 60 seconds, ensuring that the internal copper windings have reached isothermal steady state with the bath.
Because copper is encapsulated within a protective metal sheath, finite thermal conduction latency requires steady-state holding time before recording resistance.
Record the stabilized bath temperature T (in °C) and the corresponding four-wire resistance reading R (in Ω). Re-energize the heater to raise the bath temperature sequentially to 40.0 °C, 60.0 °C, 80.0 °C, and 100.0 °C (boiling point), recording the equilibrium resistance at each station.
Sampling evenly spaced thermal stations across the entire 0 °C to 100 °C range provides a uniform leverage baseline for linear regression analysis.
Tabulate the paired observations of temperature T (horizontal axis x) and coil resistance R (vertical axis y). Compute the ordinary least-squares linear regression coefficients to determine the slope m = ΔR/ΔT (in Ω °C⁻¹) and the vertical intercept b (in Ω).
Linear regression over all six temperatures averages out thermometer parallax and digital bridge quantization scatter, isolating the pure linear rate of change.
Calculate the temperature coefficient of resistance as α = m / b. Compute the inferred absolute zero of electrical resistance by extrapolating the best-fit line to R = 0 (T_abs = −b / m = −1 / α), and compare the experimental values against standard copper reference tables.
Extrapolating to zero resistance highlights the fundamental connection between classical electron-phonon scattering and the thermal energy scale.
Points are your observations. The fit uses SI x and y values before display scaling.
| # | Bath temperature T (°C) | Coil resistance R (Ω) | Temperature T (°C) | Resistance R (Ω) | Remove |
|---|
No readings yet. Take a virtual measurement and record it.