Question

In a common demonstration, a bottle is heated, and stoppered with a hard-boiled egg that’s a little bigger than the bottle’s neck. When the bottle is cooled, the pressure difference between inside and outside forces the egg into the bottle. Suppose the bottle has a volume of 0.500 L, and the temperature inside it is raised to 80.0°C while the pressure remains constant at 1.00 atm because the bottle is open.

(a) How many moles of air are inside? (b) Now the egg is put in place, sealing the bottle. What is the gauge pressure inside after the air cools back to the ambient temperature of 25°C but before the egg is forced into the bottle?

Answer 1

In this demonstration, the pressure difference between the inside and outside of a bottle forces a hard-boiled egg into the bottle when it is cooled. The number of moles of air inside the bottle can be calculated using the ideal gas law. The gauge pressure inside the bottle after cooling can also be calculated using the ideal gas law.

Step-by-step explanation:

In this common demonstration, a bottle is heated and stoppered with a hard-boiled egg that's slightly larger than the bottle's neck. When the bottle is cooled, the pressure difference between the inside and outside forces the egg into the bottle. The pressure inside the bottle before the egg is forced in can be calculated using the ideal gas law.

(a) To find the number of moles of air inside the bottle, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. Rearranging the equation to solve for n, we have n = PV/RT.

(b) To find the gauge pressure inside the bottle after the air cools back to the ambient temperature of 25°C, we can use the ideal gas law again. The gauge pressure can be calculated using the equation P = (n/V)RT, where P is the gauge pressure, n is the number of moles, V is the volume, R is the ideal gas constant, and T is the temperature. Rearranging the equation to solve for P, we have P = (n/V)RT.