= Daniell cell voltage and load experiment
{c}
The motivating observation is that a <chemical reaction> can produce a signed electrical reading even when its reacting materials occupy separate vessels. UC San Diego's teaching demonstration places a <copper> strip in $0.1\,\mathrm{mol\,L^{-1}}$ $\mathrm{CuSO_4}$ and a <zinc> strip in $0.1\,\mathrm{mol\,L^{-1}}$ $\mathrm{ZnSO_4}$, using two $400\,\mathrm{mL}$ beakers with about $300\,\mathrm{mL}$ of <chemical solution> in each. The strips connect to a voltage meter. Initially there is no ionic connection; the demonstration specifies a zero reading. A filter-paper <salt bridge> containing aqueous $\mathrm{Na_2SO_4}$ then connects the <chemical solutions>. With the meter's positive lead on <copper> and negative lead on <zinc>, its reported readings are about $+1.1\,\mathrm V$; exchanging the leads reverses the reading. These are observations reported by the university, not data generated for this article. See https://chemistryandbiochemistry.ucsd.edu/undergraduate/teaching-labs/demos/demo9b[UC San Diego, demonstration 9B: apparatus, bridge control and meter polarity].
The controls answer different questions. Exchanging only the meter leads checks the sign convention; it does not reverse the <chemical reaction> or swap the <anode> and <cathode>. Interrupting only the <salt bridge> tests the need for an ionic return path. Its absence prevents sustained cell <electric current>, but a very high-input-resistance meter may still show a transient or unstable reading while interfaces store <electric charge>. The zero reading specified for the university's apparatus is therefore not a universal theorem for every meter. Reconnecting the same <salt bridge> distinguishes a reversible interruption from a disconnected wire or exhausted <chemical solution>. This interpretation follows from <electric charge conservation> in a model allowing interfacial <electric charge> storage; see https://goldbook.iupac.org/terms/view/I03068[IUPAC Gold Book: integral capacitance of an electrode] for the <capacitance> associated with <electrode> charge.
To distinguish terminal <electric potential difference> from delivered <power>, compare the nearly open-circuit reading with readings across a known <resistor> load. In the nearly open-circuit condition, a meter with input <electrical resistance> much larger than the cell's effective internal <electrical resistance> draws little <electric current>. With a load, measure its terminal <electric potential difference> $V$ and infer $I=V/R$ using <Ohm's law>; track the readings over <time> and repeat the nearly open-circuit reading afterwards. Keep the <temperature>, <chemical solution> compositions, immersed <electrode> areas, bridge geometry and electrical contacts comparable. This is a model-based extension of the documented demonstration, not a claim that UC San Diego published a load sweep. A finite-current drop can reflect ionic <electrical resistance>, changes of interfacial <reaction rates>, or depletion near an <electrode>; a single voltage reading cannot identify which dominates. The interfacial and composition contributions are distinguished in https://goldbook.iupac.org/terms/view/O04358[IUPAC Gold Book: overpotential] and https://goldbook.iupac.org/terms/view/C01230[IUPAC Gold Book: concentration overpotential]{ref}.
For a deliberately simplified calculation, model the cell by a constant <electromotive force> $\mathcal E$ in series with a constant internal <electrical resistance> $r$, and a passive load $R>0$. Take $I$ positive from the <cathode> through the load to the <anode>. Then
$$
I=\frac{\mathcal E}{R+r},\qquad V=IR=\mathcal E-Ir,\qquad P_{\rm load}=IV=I^2R.
$$
The nearly open-circuit limit $R\to\infty$ gives $V\to\mathcal E$ but $I\to0$ and $P_{\rm load}\to0$. A straight $V$-versus-$I$ line is a prediction of constant $r$, not a general law for <electrochemistry>. See https://openstax.org/books/university-physics-volume-2/pages/10-1-electromotive-force[Ling, Sanny and Moebs, University Physics II, §10.1: internal resistance, terminal voltage and load].
\Image[/galvanic-electrodes-load-budget.png]
{title=Toy <Daniell cell> load calculation: terminal <electric potential difference>, <electric charge> and available <work>}
{description=Calculated line and energy bars, not measurements. Chosen inputs are $\mathcal E=1.10\,\mathrm V$, $r=100\,\Omega$, $R=100\,\Omega$ and a $600\,\mathrm s$ interval. The fixed-composition approximation and unit efficiency for the two intended <half-reactions> are assumed. The open-circuit marker is an ideal limit; no fit to experimental data is made.}
For the chosen values, $I=5.50\,\mathrm{mA}$ and $V=0.550\,\mathrm V$. Holding these toy parameters fixed for $600\,\mathrm s$ gives transported <electric charge> $Q=It=3.30\,\mathrm C$ and an <extent of reaction> $\xi=Q/(2F)\simeq17.1\,\mathrm{\mu mol}$, assuming all the <electric current> serves the two specified <half-reactions>. The same $\xi$ counts <zinc> consumed and <copper> deposited, rather than equal <masses>. The energy budget is
$$
\mathcal E Q=3.630\,\mathrm J
=\underbrace{VQ}_{1.815\,\mathrm J\text{ delivered to load}}
+\underbrace{I^2rt}_{1.815\,\mathrm J\text{ internal dissipation}}.
$$
The load's electrical <work> also becomes <Joule heating> when the load is a <resistor>. Here $\mathcal E Q$ accounts for the reaction's available reversible electrical <work>; a full cell thermal budget would also require its thermodynamic <entropy> contribution. Real measurements need uncertainty estimates, a specified meter input <electrical resistance> and calibration, and allowance for changing composition and unwanted <chemical reactions>. The toy value $r=100\,\Omega$ is not a measured property of the university's cell.
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