Egg In Milk Bottle Experiment Pressure Calculing Pressure

Estimate inside pressure drop, pressure difference, and net force pushing the egg into the bottle.

Expert Guide: Egg in Milk Bottle Experiment Pressure Calculing Pressure

The egg in milk bottle demonstration is one of the most effective classroom experiments for showing how air pressure can do real mechanical work. Most people describe it as a “vacuum effect,” but the physics is more precise: the pressure inside the bottle falls below the outside atmospheric pressure, so the higher outside pressure pushes the egg inward. If you want to move beyond the visual trick and actually calculate the pressure forces, this guide gives you the full framework.

In a typical setup, a burning paper strip is dropped into a bottle and a peeled hard-boiled egg is placed at the opening. The flame briefly heats the air and can change gas composition. Once the flame goes out, the trapped gas cools quickly. Lower temperature plus reduced gas moles means lower internal pressure. When the pressure difference is large enough, the net force across the bottle opening deforms the egg and drives it inside.

Why pressure calculations matter

• They convert a “magic trick” into quantitative physics.
• They let you predict whether a given bottle neck and egg size will work.
• They help compare outcomes at different weather conditions and altitudes.
• They support safer classroom procedures by avoiding excess heat or overly tight fits.

Core physics model used by the calculator

At the start, inside pressure is close to ambient pressure. For fast engineering estimates, use the ideal gas relation in ratio form:

P_in,final = P_ambient x (n_final/n_initial) x (T_final/T_initial)

Where temperature must be in Kelvin and mole ratio represents how much gas remains trapped after combustion and cooling. In this calculator, the “Estimated Gas Mole Loss (%)” input approximates how much of the initial gas amount is effectively removed from pressure contribution.

Once internal pressure is estimated, pressure difference is:

Delta P = P_ambient – P_in,final

Then force on the egg at the neck opening:

F = Delta P x A

with area A = pi x (d/2)² and pressure in pascals. Because 1 kPa = 1000 Pa, convert properly before multiplying.

Step-by-step interpretation of the experiment

1. Initial state: Bottle interior and room are near pressure equilibrium.
2. Heating phase: Combustion heats the trapped air, briefly raising internal pressure and pushing some gas out around the egg.
3. Oxygen consumption: Burning reduces oxygen fraction and changes gas composition.
4. Cooling phase: Temperature drops rapidly once flame extinguishes; pressure falls.
5. Net inward force: Outside atmospheric pressure exceeds inside pressure and pushes egg through the neck.

Real atmospheric statistics that influence your result

External atmospheric pressure is not constant. A class at sea level on a high-pressure day can get noticeably stronger inward force than a class at higher elevation with lower ambient pressure.

Altitude (m)	Standard Atmospheric Pressure (kPa)	Pressure Relative to Sea Level
0	101.325	100%
500	95.46	94.2%
1000	89.88	88.7%
1500	84.56	83.5%
2000	79.50	78.5%
3000	70.11	69.2%

These standard-atmosphere values mean the same temperature drop in the bottle produces less absolute force at high altitude because the outside pressure “push” is smaller. If your experiment seems weaker in mountain locations, this is expected.

Real composition statistics for dry air

The bottle starts with air that is mostly nitrogen and oxygen, with small fractions of argon and carbon dioxide. Oxygen is a key species because it is consumed during combustion.

Gas Component	Typical Volume Fraction in Dry Air	Relevance to Experiment
Nitrogen (N2)	78.08%	Largely inert in this setup; main bulk gas.
Oxygen (O2)	20.95%	Consumed by flame, reducing effective moles.
Argon (Ar)	0.93%	Inert trace gas.
Carbon Dioxide (CO2)	About 0.04% (variable)	Produced by combustion; contributes to pressure if retained.

In practice, not all oxygen is consumed, and not all products remain in the same thermodynamic state, so this calculator uses an adjustable mole-loss estimate for a practical engineering approximation.

Worked calculation example

Suppose ambient pressure is 101.325 kPa, initial trapped-gas temperature is 80 degrees Celsius, final temperature is 25 degrees Celsius, and estimated gas mole loss is 3%. Use a neck diameter of 3.6 cm.

• Convert temperatures to Kelvin: T1 = 353.15 K, T2 = 298.15 K
• Mole ratio: n2/n1 = 0.97
• Inside pressure: P_in = 101.325 x 0.97 x (298.15 / 353.15) = about 83.0 kPa
• Pressure difference: Delta P = 101.325 – 83.0 = about 18.3 kPa
• Neck area: A = pi x (0.036/2)^2 = about 0.00102 m^2
• Force: F = 18,300 Pa x 0.00102 m^2 = about 18.7 N

A force around 18 to 19 N is often enough to pull a compliant peeled egg through a smooth neck, depending on lubrication, egg size, and edge geometry. This is why a small pressure drop can create a dramatic visual result.

How to improve calculation quality in class or lab

• Measure bottle neck inner diameter accurately with calipers.
• Record room pressure with a barometer or weather station reading in kPa.
• Use realistic starting gas temperature. Air near the flame can be much hotter than room air.
• Run repeated trials and average results instead of relying on one test.
• Document egg mass, egg circumference, and bottle neck friction conditions.

Common mistakes in pressure calculing pressure

1. Using Celsius directly in gas-law ratios instead of Kelvin.
2. Forgetting to convert kPa to Pa before force calculation.
3. Assuming “perfect vacuum” forms inside the bottle.
4. Ignoring gas escape during heating and cooling transitions.
5. Using outer neck diameter instead of inner opening diameter.

Safety and teaching notes

This demonstration uses open flame and hot gases, so safety controls are essential. Keep a heat-resistant surface, eye protection, and a clear burn protocol. Do not use cracked glass bottles. Avoid flammable solvents for “faster ignition.” If demonstrating for younger students, perform the flame phase behind a shield and let students handle only the calculation and observation portions.

A pressure demonstration can be performed with less thermal risk by using warm water and cooling methods, but the classic burning-paper version remains popular for showing rapid pressure transitions.

How to read the calculator chart

The chart compares ambient pressure, estimated final internal pressure, and pressure difference. A higher Delta P bar means stronger predicted inward push. You can adjust the final temperature and mole loss values to model different combustion intensities and cooling speeds. This makes the page useful not only as a calculator but also as a parametric teaching tool.

Authoritative references

For deeper verification of the pressure and atmosphere assumptions, review these authoritative sources:

• NASA (.gov): Standard atmosphere overview and pressure trends with altitude
• NOAA (.gov): Air pressure fundamentals and meteorological context
• MIT (.edu): Ideal gas relation and thermodynamic background

Final takeaway

The egg in milk bottle experiment is a compact example of thermodynamics, fluid mechanics, and measurement science. When you calculate pressure instead of just watching the result, you can predict force, explain trial-to-trial variation, and connect a classic demonstration to real engineering methods. Use the calculator above to tune assumptions, compare scenarios, and build a stronger data-driven explanation of why the egg moves.