Question

In the movie Cool Hand Luke (1967), Luke wagers that he can eat 50 eggs in one hour. The prisoners and guards bet against him, saying, "Fifty eggs gotta weigh a good six pounds. A man's gut can't hold that." A peeled, chewed chicken egg has a volume of approximately \(53 \mathrm{~mL}\). If Luke's stomach has a volume of 4.2 quarts, does he have any chance of winning the bet?

Short answer

Luke's stomach, with a volume of 4.2 quarts, can hold approximately 3974.67 mL. Fifty eggs have a total volume of 2650 mL, which is less than the volume capacity of his stomach. Therefore, Luke theoretically has a chance of winning the bet.

Step-by-step solution

Convert eggs' volume to consistent units

First, we need to determine the total volume of 50 eggs. Since each egg has a volume of approximately 53 mL, we multiply 53 mL by 50 to find the total volume of eggs that Luke intends to eat. Which would give us the volume in milliliters (mL).

Convert Luke's stomach volume to milliliters

Luke's stomach volume is given in quarts, so we will convert this volume to milliliters (mL) for consistency with the volume of the eggs. There are approximately 946.35 mL in a quart, so we multiply Luke's stomach volume by 946.35 to get the volume in milliliters.

Compare the volumes

Finally, we will compare the total volume of 50 eggs with the converted volume of Luke's stomach to determine if Luke has a chance of winning the bet. If the total volume of the eggs is less than or equal to the volume of Luke's stomach, then theoretically, it could be possible for him to win the bet.

Key concepts

Volume Conversion

Let us uncover the process of volume conversion, which is crucial in various scientific contexts, including chemistry. Volume conversion is the act of translating a quantity of three-dimensional space from one unit to another. In the context of our problem, we have volumes in both milliliters (mL) and quarts.

To compare amounts readily, it's essential to convert these measures to a shared unit. As in the solution, the volume of Luke's stomach is given in quarts but needs to be compared to the volume of eggs, which is given in milliliters. The conversion factor between quarts and milliliters, approximately 946.35 mL/quart, is used to make this transition. The conversion is simple: multiply the volume in quarts by this factor to switch into milliliters. Understanding and performing volume conversion accurately is a vital skill, enabling clear communication and accurate comparisons in scientific problem-solving.

Unit Conversion

Mastering unit conversion is fundamental for proficiency in scientific studies, especially in chemistry, where various units are used to measure substances. Unit conversion is the process of exchanging one type of unit for another without altering the quantity's value.

Units of volume, mass, and length, among others, often require such conversions. The key to a successful unit conversion is the use of precise conversion factors – a binding link that equates two different units. For instance, knowing that there are 2.54 centimeters in an inch allows for the conversion of lengths from inches to centimeters and vice versa. An awareness of the most common conversion factors, as demonstrated in the egg volume problem, proves invaluable in problem-solving across the scientific field. It's paramount to apply these correctly to ensure accuracy in calculations.

Problem-solving in Chemistry

Effective problem-solving in chemistry often necessitates a methodical approach. This science deals with matter's properties and the transformations it undergoes, which often involves precise quantitative analysis.

Firstly, a problem must be clearly defined; in the case of the egg wager, the challenge is to ascertain whether a specified volume of eggs can fit within the stomach's volume. Next, relevant information is identified and organized – here, we need the volume of one egg and Luke's stomach. Following this, units are standardized to allow for direct comparison, compelling the conversion of quarts to milliliters. Finally, calculations are performed, and conclusions are drawn. Understanding and following these systematic steps can greatly increase one's efficiency and accuracy in tackling chemistry-related problems.

Stoichiometric Calculations

Diving deeper into chemistry, stoichiometric calculations are at the heart of chemical problem-solving. Stoichiometry involves quantitative relationships within a chemical reaction, often dealing with the mass, moles, and volumes of reactants and products.

In the provided example, stoichiometry isn't directly applied since we're not dealing with a chemical reaction. However, the problem-solving approach is related. A stoichiometric problem is solved step by step, starting with the balanced chemical equation. Then, conversion factors, based on mole ratios from the equation, are employed to switch between mass, volume, or particle counts of the substances involved. Although our current scenario is a physical rather than chemical problem, the logical sequence and necessity for unit consistency are common threads between this and stoichiometric calculations. The key lessons from stoichiometry - meticulous approach, unit conversions, and ratio application - are universally applicable in chemical problem-solving.