A physical investigation on the phenomenon of the Dancing Coin

TL;DR

This paper investigates the cyclic movement of a coin on a cold bottle's neck caused by internal gas expansion, providing a quantitative analysis through experiments and modeling based on thermodynamics principles.

Contribution

It offers the first quantitative model of the phenomenon using ideal gas assumptions, Newton's law of cooling, and numerical simulations, validated by experiments.

Findings

The model accurately predicts the coin movement cycle.

Experimental data confirms the theoretical pressure and temperature evolution.

The study enhances understanding of thermodynamic demonstrations.

Abstract

When a coin is placed on the neck of a cold bottle, the coin will move cyclically. This is caused by the expansion of the gas inside the bottle warming up, which will cause the coin to rise when the internal pressure is large enough to overcome the weight of the coin. This problem, widely used to qualitatively demonstrate several laws of thermodynamics, has no quantitative solution in the literature. For this we use the ideal gas model and Newton's law of cooling combined with computational numerical simulations and systematic experimental measures to confront our theoretical model, including equations for the evolution of temperature, pressure and behaviour of the coins in the system.