Popping Under Pressure: The Physics of Popcorn Paul V. Quinn, Sr. Advisor Sally Warner Teaching Assistant Alex Arkhipov Carly Becker Dave Bergamo Veronica Demtchouk Andrew Freddo Ted Kreider Mike Lee Joe Montalbano Dave Richards Liz So Jasper Wang

History of Popcorn Introduced by Native Americans Aztecs used for decoration Oldest popcorn 4,000 years old In 20 th century, business grew

Industrial Facts Americans consume 17 billion quarts annually. 54 quarts per family 1 million kernels remain unpopped

Industry Standards 10-12% kernels unpopped Flake size: 5-7 cm 3 /kernel Average diameter: 2.25 cm cm 3 /g

Essential Elements of a Popcorn Kernel

Inner Moisture Need 16%-20% moisture to pop Moisture turns into steam and expands Internal pressure increases Popping depends on how heat is distributed to the moisture in the starch

The Shell Locks moisture inside the kernel Heated moisture leads to pressure buildup The shell ruptures

Starch When the kernel explodes: Gelatinized starch expands into thick, jelly-like bubbles Neighboring bubbles fuse together Bubbles solidify

Thermodynamics Water vapor is an ideal gas Vapor expands adiabatically where

Thermodynamics Variable of interest V f To maximize V f, must minimize P f

Theoretical Model Goal: Approximate maximum value for R v n proportional to the difference in P Assume proportion of 1:1

Finding the Radius Assume and When, is maximized Solving gives

Dependence on Pressure As pressure decreases, volume increases

Numerical Approximation Euler’s Method Fit curve

The Hot Plate Apparatus

The Microwave Apparatus

Procedure Kernels sorted Kernels counted before and after popping Trials run under varying pressures Different trials: –With oil, with mesh, dry; with bag, without bag –Alter sample size: 10 g, 20 g, 40 g

Procedure After each trial, we: –Found the volume of the popped kernels –Counted the popped and unpopped kernels –Calculated values for the three variables, σ, π, and ω

Variables σ = total popped volume (cm 3 ) original sample weight (g) π = the total popped volume (cm 3 ) number of popped kernels ω = the number of unpopped kernels original number of kernels

Results 70 Trials 8921 Kernels: –862 Unpopped –8059 Popped Total Volume: cm 3 Reduced Pressure: –Less waste (lower ω) –Larger flake size (higher π) –Larger volume per gram (higher σ)

Hot Plate - ω

Hot Plate - π

Hot Plate - σ

Microwave - ω

Microwave - π

Microwave - σ

Hot Plate Variable Pressure - ω

Hot Plate Variable Pressure - π

Hot Plate Variable Pressure - σ

Conclusions Pressure decreases: →ω decreases →π increases →σ increases Improved ω Matched values of σ and π The more packed the bag, the more restricted the expansion

Sources of Error Subjectivity Non-ideal conditions Equipment defects Varied portions of experiment: –Temperature of hot plate –Popping time –Amount of oil –Age of popcorn

If We Had More Time... We would use spherical harmonics Use more brands and sample sizes Get better equipment like: – Different microwaves – Vacuum pump that reduces pressure below 1/30 atm –Better weather stripping

The End Are there any questions?