Egg In Milk Bottle Experiment Pressure Calculations

Estimate internal pressure drop, suction force at the bottle neck, and whether pressure can overcome egg weight plus insertion resistance.

How to Calculate Pressure in the Egg in Milk Bottle Experiment

The egg in milk bottle experiment is one of the best demonstrations of atmospheric pressure and gas behavior. In the classic setup, a lit paper strip or similar heat source warms the air in a bottle, a peeled hard boiled egg is placed at the bottle opening, the flame goes out, and the egg gets pulled inward. Many people describe this as suction, but the more accurate explanation is pressure difference. Air pressure outside the bottle stays comparatively higher while pressure inside the bottle drops, so the outside atmosphere pushes the egg into the neck.

If you want quantitative results, not only a visual demo, pressure calculations let you estimate exactly how much force acts on the egg. This matters in classrooms, science fairs, and STEM labs where you want repeatable data and clear scientific reasoning. The calculator above uses a practical model based on the ideal gas relationship and estimates for oxygen loss during combustion.

The Physics Model Behind the Calculator

1) Pressure, temperature, and moles in a closed volume

The ideal gas law is written as P V = n R T. In this experiment, bottle volume is roughly constant during the short time between heating and cooling, so pressure is proportional to both absolute temperature and gas amount. As heated air cools, T decreases, lowering pressure. Also, combustion consumes oxygen and produces hot products that partially escape before the egg seals, reducing effective n. Both effects reduce inside pressure.

For educational calculations, a useful simplified estimate is:

P_inside ≈ P_outside × (1 – mole loss fraction) × (T_cool,K / T_hot,K)

This approximation matches observed behavior well enough for classroom predictions, especially if you treat oxygen and mole loss as an estimated percentage between 2% and 10%, depending on flame size, bottle geometry, and timing.

2) Converting pressure difference into force on the egg

Once you estimate inside pressure, the driving pressure difference is:

ΔP = P_outside – P_inside

Pressure force at the neck is:

F_pressure = ΔP × A, where A = π(d/2)²

Here, neck diameter d must be in meters and pressure in pascals. Then compare this force to resisting forces:

• Egg weight: m g
• Contact and friction resistance at the bottle mouth
• Any deformation resistance from the egg white

If pressure force exceeds these resistances, the egg moves into the bottle.

Step by Step Calculation Workflow

1. Measure bottle neck inner diameter in centimeters.
2. Measure egg mass in grams, or use a known average for your egg size class.
3. Estimate hot internal air temperature after brief flame heating.
4. Set the final internal temperature near room temperature.
5. Choose local atmospheric pressure by elevation preset or custom value.
6. Estimate oxygen and net mole loss percentage due to combustion and venting.
7. Estimate resistance force at the neck, based on prior trials.
8. Run the calculation, inspect pressure and force values, then compare prediction to real trial outcome.

Reference Data Table: Atmospheric Pressure by Elevation

Atmospheric pressure changes strongly with elevation, and this directly changes experiment performance. Lower outside pressure means lower maximum available push on the egg. The values below are standard atmosphere approximations widely used in meteorology and engineering.

Elevation (m)	Approx Pressure (kPa)	Pressure (atm)	Relative to Sea Level
0	101.3	1.000	100%
500	95.5	0.943	94.3%
1000	89.9	0.887	88.7%
1500	84.6	0.835	83.5%
2000	79.5	0.785	78.5%

Reference Data Table: Common Egg Mass Values

Egg mass changes both weight resistance and how much deformation is needed to pass through the neck. The table below uses commonly cited U.S. retail class averages derived from official weight classes.

U.S. Egg Size	Dozen Weight Class (oz)	Approx Average per Egg (g)	Approx Weight Force (N)
Medium	21 oz/dozen	49.6 g	0.49 N
Large	24 oz/dozen	56.7 g	0.56 N
Extra Large	27 oz/dozen	63.8 g	0.63 N
Jumbo	30 oz/dozen	70.9 g	0.70 N

Worked Example for a Typical Classroom Trial

Suppose you use a standard milk bottle with a 3.2 cm neck, a large egg at 56.7 g, outside pressure of 101.3 kPa, hot internal air at 80°C, cooled internal air at 22°C, and estimated mole loss of 4%.

• Convert temperatures: 80°C = 353.15 K, 22°C = 295.15 K.
• Inside pressure estimate: 101.3 × 0.96 × (295.15 / 353.15) ≈ 81.3 kPa.
• Pressure difference: 101.3 – 81.3 = 20.0 kPa.
• Neck area: d = 0.032 m, A = π(0.016)² ≈ 0.000804 m².
• Pressure force: 20,000 Pa × 0.000804 ≈ 16.1 N.
• Egg weight: 0.0567 × 9.81 ≈ 0.56 N.

Even with a few newtons of insertion resistance, 16 N is usually more than enough to push the egg inward. This is why the demonstration tends to be dramatic when setup and timing are good.

Why Real Results Can Differ from Your Calculations

Heat transfer timing

If the egg is placed too late, air may cool before the seal forms, reducing the pressure differential. If placed too early, not enough heating may occur.

Seal quality at the opening

A perfect temporary seal makes pressure difference effective. A leaky seal allows equalization, reducing force.

Bottle geometry and glass thickness

Neck lip shape changes local contact pressure and friction. Two bottles with similar diameters can still produce different results.

Egg preparation differences

Hard boiled eggs vary in moisture, surface texture, and stiffness. A slightly wet egg can reduce friction and improve entry consistency.

How to Use the Chart Output

The chart compares outside pressure, predicted inside pressure, pressure difference, and force components. This gives a fast visual check:

• If inside pressure bar is much lower than outside, the pressure mechanism is strong.
• If pressure force bar is higher than required force bar, egg entry is likely.
• If bars are close, small setup differences can decide success or failure.

Safety, Good Lab Practice, and Data Quality

1. Use heat resistant gloves and eye protection during flame handling.
2. Keep flammable materials away from the bench area.
3. Use adult supervision in K to 12 settings.
4. Do not use cracked glass bottles.
5. Collect at least 5 repeated trials for meaningful average results.
6. Record room temperature and local pressure for each run.
7. Use the same bottle and egg size class to reduce variability.

Authoritative Sources for Deeper Study

For high quality background references, review these official resources:

• NOAA JetStream, atmospheric pressure fundamentals
• NASA Glenn, ideal gas equation and state variables
• NIST SI units reference, standards for scientific calculations

Conclusion

The egg in milk bottle experiment is not magic, it is a clear demonstration of pressure gradients acting over area. With a simple computational model, you can predict whether an egg should move, compare trials across elevations, and quantify why one setup works better than another. Use the calculator as a planning and analysis tool, then validate with measured trials. That combination, theory plus experiment, is what turns a classic demo into a true physics investigation.