Why Do Soda Cans Explode When Shaken? Understanding the Relation to Fluid Stress

When a soda can is shaken, it experiences an increase in pressure due to the formation of small bubbles in the liquid. This is because shaking introduces energy into the system, causing the gas in the soda to come out of solution and form bubbles. These bubbles then provide an easier pathway for the dissolved gas to escape, leading to a more rapid release of carbon dioxide when the can is opened.

Understanding the Ideal Gas Law and Pressure Generation

One way to quantify this phenomenon is through the use of the ideal gas law, which describes the relationship between the pressure, volume, and temperature of a gas. The ideal gas law is expressed as:

P = (n * R * T) / V

Where:
– P is the pressure of the gas (in Pascals)
– n is the number of moles of the gas (in moles)
– R is the universal gas constant (8.314 J/mol·K)
– T is the absolute temperature of the gas (in Kelvin)
– V is the volume of the gas (in cubic meters)

In the case of a soda can, we can use the ideal gas law to calculate the pressure that would be generated if all of the dissolved carbon dioxide were to come out of solution and form a gas. Assuming a typical can of soda contains about 2.2 grams of carbon dioxide and the “air gap” in the soda can is about 5 milliliters, we can calculate the following:

• Mass of CO2 in the can: 2.2 grams
• Molar mass of CO2: 44.01 g/mol
• Number of moles of CO2: 2.2 g / 44.01 g/mol = 0.05 mol
• Volume of the air gap: 5 mL = 5 × 10^-6 m^3
• Assuming room temperature (20°C = 293.15 K)

Plugging these values into the ideal gas law equation:

P = (0.05 mol × 8.314 J/mol·K × 293.15 K) / (5 × 10^-6 m^3)
P ≈ 24 MPa

This pressure is significantly higher than the pressure that a soda can is designed to withstand, which is typically around 0.6-0.8 MPa. For comparison, the pressure in a scuba diving cylinder is about 20 MPa, and scuba cylinders are much stronger than soda cans. Therefore, it is clear that shaking a soda can can generate enough pressure to cause the can to explode if all of the carbon dioxide were to come out of solution and form a gas.

Understanding Fluid Stress and Shaking-Induced Effects

In addition to the pressure generated by the formation of gas bubbles, shaking a soda can can also cause the can to experience fluid stress. Fluid stress is the force that is exerted on a solid object by a fluid, and it is determined by the pressure and velocity of the fluid. In the case of a soda can, the fluid stress is caused by the movement of the liquid inside the can, which is subjected to acceleration due to the shaking motion.

The fluid stress experienced by a soda can can be quantified using the Navier-Stokes equations, which describe the motion of fluid. These equations take into account the pressure, velocity, and viscosity of the fluid, as well as the shape and motion of the object that is immersed in the fluid. By solving the Navier-Stokes equations for a soda can that is being shaken, it is possible to calculate the fluid stress that the can is experiencing.

One study found that shaking a soda can vigorously can cause a temperature rise due to viscous damping in the fluid. This temperature rise is caused by the friction between the liquid and the walls of the can, and it can lead to an increase in the pressure inside the can. The study also found that the fluid stress experienced by the can can cause the can to become more solid due to the pressure, and that the can can eventually fatigue due to shaking-induced cyclic fatigue.

Factors Affecting Soda Can Explosion

Several factors can influence the likelihood and severity of a soda can explosion when shaken:

1. Carbon Dioxide Content: The amount of dissolved carbon dioxide in the soda is a key factor. Cans with higher CO2 content will generate more pressure when shaken.

2. Can Volume and Headspace: The volume of the can and the size of the air gap (headspace) above the liquid can affect the pressure buildup. Smaller cans and less headspace can lead to higher pressures.

3. Shaking Intensity and Duration: More vigorous and prolonged shaking introduces more energy into the system, leading to more bubble formation and pressure increase.

4. Can Material and Design: The strength and structural integrity of the can itself can determine how much pressure it can withstand before failing.

5. Temperature: Higher temperatures can increase the solubility of CO2 in the liquid, leading to more gas coming out of solution when shaken.

6. Liquid Viscosity: The viscosity of the soda can affect the fluid stress and heat generation within the can during shaking.

Conclusion

In summary, shaking a soda can can generate enough pressure and fluid stress to cause the can to explode if all of the carbon dioxide were to come out of solution and form a gas. This phenomenon can be quantified using the ideal gas law and the Navier-Stokes equations, which describe the relationship between the pressure, volume, temperature, and motion of a gas and a fluid, respectively. Understanding the factors that influence soda can explosions is crucial for designing safer and more robust containers for carbonated beverages.

References:
– Why Does a Shaken Soda Fizz More Than an Unshaken One? (n.d.). Scientific American. Retrieved July 13, 2024, from https://www.scientificamerican.com/article/why-does-a-shaken-soda-fi/
– Can a Soda Can Be Shaken Up to the Point That It Explodes? (2015, June 26). Reddit. Retrieved July 13, 2024, from https://www.reddit.com/r/askscience/comments/3b607e/can-a_soda_can_be_shook_up_to_the_point_that_it/
– Is a Beverage Sealed in a Depressurized, Squishy-Feeling Soda/Pop Can Safe to Drink, and How Does It Get That Way? (2018, February 13). Reddit. Retrieved July 13, 2024, from https://www.reddit.com/r/answers/comments/7x68vu/is_a_beverage_sealed_in_a_depressurized_squishy/