This Simple Lab Engine Teaches More Than Your Textbook

Why bother building a tiny, inefficient engine?

Because the inefficiency is the whole story.

On paper, a heat engine is simple: take heat from a hot source, turn part of it into work, dump the rest to a cold sink. The efficiency is just

\[\eta = \frac{W}{Q_\text{in}}\]

and in ideal-land you compare it to the Carnot limit:

\[\eta_\text{Carnot} = 1 - \frac{T_\text{cold}}{T_\text{hot}}\]

with temperatures in kelvin.

In the lab, though, students like Maya—second‑year physics major, pretty sharp, pretty skeptical—quickly notice something. Her neat calculation says the engine could reach, say, 35% efficiency. The data she gets after an hour of careful measurements? More like 7%. At first she thinks she messed up the math. Then she realizes: this is the lesson.

The gap between theoretical and measured efficiency is where friction, turbulence, heat leaks, and sloppy insulation all show up. If you design your experiment well, you don’t just “prove a formula.” You actually see why real engines—car engines, power plants, refrigerators running in reverse—never hit their theoretical limits.

So how do you set this up without turning your lab into a sauna?

A tabletop Stirling engine that actually does work

If you’ve ever seen one of those tiny glass or aluminum engines spinning on top of a cup of hot water, that’s a Stirling engine. It’s a closed‑cycle heat engine that runs on a temperature difference, not on combustion inside the cylinder. Perfect teaching tool—if you treat it like more than a toy.

What the basic Stirling experiment looks like

You place the Stirling engine on a hot reservoir (often a beaker of hot water or an electric hot plate set to a safe temperature) and expose the top to room air or an ice bath. The temperature difference makes the piston move, and a flywheel spins.

Now the interesting part: turning that spinning flywheel into a measurable output.

Maya’s lab group did something that looks almost too simple: they attached a small pulley to the flywheel and ran a thread over it to a hanging mass. As the engine ran, it slowly lifted the mass. That’s mechanical work you can actually quantify.

They measured:

• Mass lifted (in kilograms) and the height it rose (in meters)
• Time it took to lift that mass
• Temperature of the hot side and cold side (in °F and °C, then converted to K for calculations)
• Power input from the hot side, estimated from the heater’s electrical power or from the cooling rate of the hot reservoir

From this, they could estimate:

• Output power: \(P_\text{out} = \frac{m g h}{t}\)
• Input power: from the electrical heater rating (say, 50 W) or from calorimetry (rate of temperature drop of hot water times its heat capacity)
• Efficiency: \(\eta = \frac{P_\text{out}}{P_\text{in}}\)

Where the real physics sneaks in

The first surprise? The engine barely lifted the mass. The second? The numbers looked terrible.

For one run, they had:

• 0.050 kg mass lifted 0.40 m in 60 s
• So \(W = m g h \approx 0.050 \times 9.8 \times 0.40 \approx 0.196 \text{ J}\)
• Over 60 s, that’s \(P_\text{out} \approx 0.0033 \text{ W}\)

The heater was drawing about 40 W.

So the measured efficiency came out around:

\[\eta_\text{measured} \approx \frac{0.0033}{40} \approx 8.3 \times 10^{-5} \; (0.008\%)\]

That’s… not great. But it’s also honest.

Then they compared it to Carnot. With

• Hot side ~ 176 °F (80 °C → 353 K)
• Cold side ~ 68 °F (20 °C → 293 K)

Carnot efficiency:

\[\eta_\text{Carnot} = 1 - \frac{293}{353} \approx 0.17 \; (17\%)\]

So the engine was running at a tiny fraction of its theoretical limit. Why? Well, start counting:

• Heat lost to the air instead of doing useful work
• Friction in the bearings and piston seals
• Poor thermal contact with the hot plate
• Energy spent just keeping the flywheel spinning

Once students start listing those losses, the messy data starts to make sense. The experiment becomes less about “finding the right number” and more about understanding why the number is small.

Steam-in-a-can: a low‑budget Rankine cycle

Not every lab has a polished Stirling engine. But almost any lab can do a stripped‑down steam engine experiment that mimics a Rankine cycle.

One instructor I know, Dr. Chen, runs what she calls the “steam-in-a-can” lab. It’s exactly what it sounds like: a small metal container with a bit of water, a tight lid, and a narrow outlet connected to a tiny turbine or even just a paddle wheel.

How it runs

• You heat the can on a hot plate until the water boils.
• Steam flows out through the outlet and spins the wheel.
• The steam then condenses in a cooled coil or just vents into a cold water bath.

You can:

• Measure electrical power into the hot plate with a wattmeter.
• Estimate heat used to generate steam from the mass of water boiled off and the latent heat of vaporization.
• Measure mechanical power out by attaching a small dynamometer or a Prony brake to the wheel.

Again, the efficiency is the ratio of useful work to heat input.

Why this experiment is messy but valuable

It’s easy to underestimate how much heat goes into simply boiling water. You can use the specific enthalpy of vaporization of water (about 2256 kJ/kg at 100 °C) and the measured mass of water lost to steam to estimate the heat input from phase change alone.

Say you boil off 0.010 kg (10 g) of water in 5 minutes:

• Heat for vaporization: \(Q \approx 0.010 \times 2{,}256{,}000 \approx 22{,}560 \text{ J}\)
• Over 300 s, that’s \(P_\text{in} \approx 75 \text{ W}\)

If the little wheel only delivers 0.5 W of mechanical power, you’re looking at

\[\eta \approx \frac{0.5}{75} \approx 0.0067 \; (0.67\%)\]

Again, it looks terrible on paper. But now you can have a very grounded discussion:

• Real power plants use high pressures and high temperatures to get closer to the Carnot limit.
• They invest serious engineering effort in turbine design and insulation.
• Your lab setup is intentionally simple and lossy, so you can see where energy disappears.

If you want to connect this to real‑world energy systems, the U.S. Energy Information Administration has data on average thermal efficiencies of fossil fuel power plants, which are often in the 30–40% range—already far below their Carnot limits.

Can you measure heat engine efficiency with just hot and cold water?

Yes—if you’re okay with an indirect approach.

Some labs don’t have engines at all. Instead, they simulate a “heat engine” using a resistive heater, a DC motor, and two water baths.

Here’s how one undergrad lab set it up:

• A resistor immersed in a hot water bath is powered by a DC supply.
• The heat from the resistor warms the water: that’s your heat input.
• A small DC motor attached to a paddle in a second water bath runs as a generator, driven by a mechanical source (or even by hand in a controlled way).
• The electrical energy from the generator is fed to the resistor.

You’ve built a crude loop: mechanical work → electricity → heat. It’s not a classical heat engine in the textbook sense, but you can track energy transfers with reasonable precision.

Students measure:

• Temperature rise of the hot bath (to get \(Q\))
• Voltage and current from the generator (to get \(W\))
• Time intervals to compute power

The efficiency calculation is the same, but here the focus shifts to measurement technique:

• How accurate is your thermometer?
• How much heat leaks to the environment during the run?
• How well mixed is the water (do you stir, or just hope for the best)?

This setup tends to give slightly better‑looking numbers, partly because the system is more controllable. But it also prompts a nice conversation: are you really measuring a heat engine, or are you measuring the efficiency of your conversion chain (mechanical → electrical → thermal)? The nuance matters if you care about thermodynamic definitions.

Why your measured efficiency will almost always disappoint you

If you go into these experiments expecting to “hit Carnot,” you’re going to be annoyed. But that disappointment is actually useful.

Think about what Carnot efficiency assumes:

• Reversible processes (no friction, no turbulence, no finite temperature differences)
• Perfect insulation
• Infinite time for each step of the cycle

Now look at your lab bench:

• Metal parts rubbing against each other
• Air currents carrying heat away
• Heat exchangers with finite surface area and sloppy contact
• Cycles running at non‑zero speed because, well, you want the engine to actually move

The point isn’t to chase a magic number. It’s to:

• Identify where losses occur (mechanical, thermal, fluid)
• Quantify them where possible (friction torque, heat leak rate)
• Compare different setups (better insulation, improved lubrication, different load)

When students like Maya tweak the experiment—wrapping the hot reservoir in better insulation, reducing mechanical load, lubricating bearings—they usually see small but real improvements in measured efficiency. Not miraculous, but enough to prove that engineering choices matter.

For a more formal treatment of heat engine limits and real‑world cycles, university thermodynamics course notes, like those from MIT OpenCourseWare, are worth a look.

Safety and sanity checks before you start heating things

Because we’re talking about hot plates, steam, and moving parts, it’s not a bad idea to be a bit paranoid.

A few guidelines instructors repeat for a reason:

• Steam burns fast. Keep hands away from vents and boiling water. Use tongs or insulated gloves when adjusting equipment.
• Pressurized containers are not toys. Never fully seal a heated container without a pressure relief path.
• Electrical safety matters. Check insulation on heater leads, avoid water near exposed connectors, and use properly rated power supplies.

For general lab safety principles, resources from the National Institutes of Health and many university EHS offices offer clear, practical guidance.

How to turn a messy efficiency lab into a strong report

The difference between a forgettable lab and a memorable one is usually in the analysis, not the apparatus.

Students who get the most out of these experiments tend to:

• Show both measured and theoretical efficiencies side by side, with clear assumptions.
• Estimate uncertainties in temperature, mass, time, and power, and propagate them into \(\eta\).
• Discuss specific loss mechanisms instead of vague “experimental error.”
• Propose realistic improvements (better insulation, different load, slower cycle, improved seals) and, if time allows, test at least one.

One clever twist I’ve seen: groups run the same Stirling engine with different cold‑side conditions—room air, ice bath, and a fan blowing across the top—and then compare not just efficiency, but also stability and power output. The data turn into a story about how temperature gradients and heat rejection actually control engine behavior.

If you want to connect this to broader energy topics, the U.S. Department of Energy has plenty of material on efficiency in power generation and engines that can help students see why their tiny lab engine is part of a much bigger conversation.

FAQ: Heat engine efficiency experiments

Why is my measured efficiency so much lower than the Carnot efficiency?

Because your system is full of irreversibilities: friction in moving parts, heat leaks to the environment, finite temperature differences in heat exchangers, and non‑ideal working fluids. Carnot efficiency is a theoretical upper bound for an ideal, reversible engine. Real lab setups usually run at a small fraction of that value.

Do I really need to convert temperatures to kelvin for efficiency calculations?

Yes, if you’re using formulas like \(\eta_\text{Carnot} = 1 - T_\text{cold}/T_\text{hot}\). Those require absolute temperatures. You can measure in °F or °C, but convert to kelvin before plugging into the equation.

Is a Stirling engine better than a steam engine for teaching efficiency?

They each have advantages. Stirling engines are compact, quiet, and safer because they operate at relatively low pressures and can run from simple heat sources. Steam setups illustrate phase change and are closer to real power plant cycles. For a first encounter with efficiency, a tabletop Stirling engine is usually easier to manage and measure.

Can I run these experiments at home?

Some simplified versions, yes—like running a small commercial Stirling engine on a mug of hot water, and roughly estimating work from lifting a light weight. But anything involving pressurized steam, improvised boilers, or mains‑powered heaters should be done in a supervised lab with proper safety protocols.

How accurate do my measurements need to be?

You don’t need ultra‑high precision to learn from these experiments. What matters more is consistency and honest uncertainty estimates. If you can measure temperatures to within about 1 °C, masses to 0.1 g, and times to 0.1 s, you’ll already be able to see the main trends and compare different configurations meaningfully.

In the end, a heat engine efficiency lab is less about chasing a perfect percentage and more about learning to ask the right questions. Where did the energy go? How do we know? And what would it take—on a lab bench or in a power plant—to get even a little closer to that stubborn theoretical limit?