Determine the coefficient of linear thermal expansion (α) of a solid copper specimen using a steam-jacketed dilatometer with precision micrometer screw gauge and electrical contact indicator, measuring the longitudinal elongation (ΔL) resulting from controlled thermal elevation (ΔT) and evaluating the linear dilatation slope. Explore a virtual apparatus, collect readings and analyse a graph.
Ready for a virtual observation.
Adjust the apparatus, then take a reading.
Readings are generated by an ideal model. The diagram is schematic and is not to scale.
The teaching simulation models linear thermal dilatation under steady-state isothermal conditions with an initial rod length L_0 = 1.0000 m at T_0 = 20.00 °C and an invariant reference expansion coefficient α = 16.80 × 10⁻⁶ K⁻¹. In physical experiments, minor temperature gradients exist along the length of the steam jacket (especially near the protruding ends), thermometer thermal lag and stem emergent column errors can cause small temperature reading offsets, mechanical micrometer backlash or pitch errors contribute displacement uncertainty (±0.002 mm), electrical contact threshold sensitivity can vary with surface oxide film formation on the copper tip, and slight frame flexion during thermal elevation can introduce small structural offsets. The simulation calculates longitudinal elongation using the linear dilatation relationship ΔL = L_0 · α · ΔT, where L_0 = 1.0000 m is the baseline length, α = 16.80 × 10⁻⁶ K⁻¹ is the reference linear expansion coefficient for pure copper, and ΔT = T − T_0 is the temperature elevation above 20.00 °C. Elongation readings are rounded to 0.001 mm to match high-precision micrometer screw resolutions, and ordinary least-squares regression of ΔL against L_0 · ΔT across five temperature stations yields the reported linear expansion coefficient.
A double-walled brass jacket 1.1 m in length mounted upon a rigid heavy cast-iron bed plate, equipped with low-friction internal guide rollers to support the specimen rod horizontally, an internal thermometer socket, a steam inlet nozzle, a bottom condensate drain, and a hardened steel fixed abutment block at the left end.
A hardened stainless steel micrometer head having a calibrated lead screw pitch of 0.500 mm and 50 circular thimble subdivisions, rigidly clamped to the right end frame to measure longitudinal specimen displacements with an instrument resolution of 0.001 mm.
A 1.5 V dry cell battery connected in series with a 10 kΩ current-limiting resistor and sensitive center-zero galvanometer between the insulated fixed frame and the micrometer spindle, providing instantaneous, zero-force visual indication when the advancing micrometer tip touches the expanding copper rod.
An electric steam generator supplying saturated water vapor at 100 °C through flexible insulated tubing to elevate the specimen temperature uniformly, monitored by a 0.1 °C immersion thermometer inserted into the central dilatometer chamber.
Determine the coefficient of linear thermal expansion (α) of a solid copper specimen using a steam-jacketed dilatometer with precision micrometer screw gauge and electrical contact indicator, measuring the longitudinal elongation (ΔL) resulting from controlled thermal elevation (ΔT) and evaluating the linear dilatation slope. Suggested independent settings: 15.0, 30.0, 45.0, 60.0, 75.0 °C.
Measure the overall length of the clean, polished copper rod at ambient room temperature using a precision steel meter scale and vernier calipers to ±0.5 mm, recording L_0 = 1.0000 m. Insert the rod into the steam jacket, seating its left end firmly against the hardened steel fixed abutment stop. Insert the calibrated thermometer into the central socket and record the steady initial room temperature T_0 = 20.00 °C.
Accurate baseline length and temperature measurements establish the fundamental thermodynamic reference state from which all subsequent longitudinal strain is evaluated.
Connect the electrical contact indicator leads to the rod and micrometer head. Slowly advance the micrometer thimble until the galvanometer needle deflects, indicating that the spindle has touched the cold rod tip without exerting compressive mechanical strain. Read the micrometer drum to ±0.001 mm and record this initial baseline reading R_0. Back the micrometer screw off by 2 to 3 turns to allow room for free expansion.
The electrical circuit ensures zero-pressure contact sensing, completely eliminating compressive deformation of the rod and flexion of the mounting frame.
Connect the steam generator to the dilatometer inlet and place a beaker beneath the drain nipple to collect condensed water. Activate the boiler and admit steam steadily into the jacket. Observe the rapid temperature rise on the central thermometer and allow steam to circulate until condensate flows smoothly and the thermometer reading stabilizes.
Uniform circulation of saturated steam sweeps air from the chamber and guarantees that the entire length of the copper rod achieves an isothermal steady state.
Once steady-state equilibrium is attained at the target temperature (e.g., T = 65.0 °C, giving ΔT = 45.0 °C), carefully advance the micrometer thimble until the galvanometer needle just twitches. Record the hot micrometer reading R_hot to ±0.001 mm. The longitudinal elongation is evaluated as ΔL = R_hot − R_0. Immediately retract the screw to prevent jamming.
Making the measurement precisely at steady-state equilibrium prevents transient temperature gradients from distorting the calculated elongation.
Repeat the measurement procedure across five distinct temperature elevations (ΔT = 15.0 °C, 30.0 °C, 45.0 °C, 60.0 °C, and 75.0 °C) by adjusting the steam-air mixing ratio or tracking the cooling curve of the jacket. For each setting, record the stable temperature elevation ΔT and corresponding micrometer elongation ΔL.
Collecting multiple data pairs across a wide thermal span verifies the linearity of the thermal dilatation law and provides statistical redundancy for regression analysis.
For each observation, calculate the independent variable X = L_0 · ΔT in m K (or m °C) and the dependent displacement Y = ΔL in meters. Plot Y against X, perform ordinary least-squares linear regression to determine the gradient S, and evaluate the linear thermal expansion coefficient α = S. Compare α with the standard reference value for electrolytic copper.
Ordinary least-squares regression averages out minor micrometer reading scatter and isolates the true linear slope independent of single-trial zero offsets.
Points are your observations. The fit uses SI x and y values before display scaling.
| # | Temperature elevation Delta T (°C) | Elongation Delta L (mm) | Product L_0 Delta T (m K) | Longitudinal elongation Delta L (m) | Remove |
|---|
No readings yet. Take a virtual measurement and record it.