Thermodynamics Laboratory

Laboratory practice to measure heat capacity and evaluate heat exchange.

Conceptual context

A thermodynamics laboratory turns energy exchange into a measurable sequence. The experiment supplies or removes $Q$, records $\delta_{T}$, and observes the response of a known $m$. The aim is not merely to obtain a number, but to identify how much energy reaches the sample, how much remains in the vessel, and how much appears as $Q_perdidas$. The practice separates temperature from energy, forces a careful definition of the system, and tests whether the response is linear. Its central question is experimental: what relationship links supplied heat to thermal change, and what $C_exp$ characterizes the real assembly?

🟢 Essential level

When a sample receives $Q$, its temperature usually changes. The size of that change depends on the amount of matter, represented by $m$, and on how easily the material stores thermal energy, described by $c$.

The same energy input produces a small $\delta_{T}$ in a system with large thermal capacity and a larger change in one that stores little energy per kelvin. In the laboratory, the measurement is repeated for several heating steps and transferred heat is plotted against temperature change. If the points form an almost straight line, the slope summarizes the response of the setup and is interpreted as $C_exp$. The experiment also shows that not all energy remains in the sample, because the vessel, sensor, and surroundings can absorb part of it. For that reason the sample should be insulated as well as possible and, when needed, the result corrected through a prior calibration of the vessel, so that $Q_perdidas$ is not mistaken for a genuine thermal property of the sample.

🔵 Formal level

Basic formulas

For a sample that does not undergo a phase change, the basic relation is:

Sensible heat

This formula connects $Q$, $m$, $c$, and $\delta_{T}$. If $m$ and $c$ remain constant, the dependence of $Q$ on $\delta_{T}$ is linear. On a Q-versus-ΔT graph, the ideal slope is the product of mass and specific heat capacity. The sign of Q should match the sign of ΔT when mass and specific heat capacity are positive.

The effective response of the setup is obtained from:

Experimental heat capacity

Real student questions

Why use kelvin if a Celsius temperature difference has the same numerical value? Because the numerical differences agree, while kelvin preserves SI consistency.

Is the slope always the specific heat capacity? No. The slope is $C_exp$. It equals mass times $c$ only when other contributions are negligible or corrected.

Why does the fit not pass exactly through the origin? Possible causes include sensor bias, heat absorbed before recording begins, or systematic $Q_perdidas$.

Is fast or slow heating better? Heating too fast creates internal gradients; heating too slowly increases environmental losses. A practical compromise is required.

Final synthesis

Transferred heat and temperature change are approximately linear when the system remains in one phase and losses are controlled. The slope defines $C_exp$, while the energy balance and residual pattern reveal whether the model truly represents the setup.