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Chapter 5: Problem 81

Discuss the following phenomena in terms of the gas laws: (a) the pressure in an automobile tire increasing on a hot day, (b) the "popping" of a paper bag, (c) the expansion of a weather balloon as it rises in the air, (d) the loud noise heard when a lightbulb shatters.

Short Answer

Expert verified
The phenomena can be explained by the gas laws as follows: (a) The increase in pressure in a tire on a hot day is due to Gay-Lussac's Law, as the pressure of gas increases with the temperature if volume is constant. (b) The 'popping' of a paper bag is due to Boyle's Law, as the pressure increases when volume decreases rapidly. (c) The expansion of a weather balloon as it rises is due to Charles's Law, with dominant influence from the decrease in external pressure. (d) The loud sound from a shattered lightbulb is a result of Boyle's Law, with gas under pressure suddenly coming into a lower pressure environment.

Step by step solution

01

Understanding Phenomena (a)

In case (a), the pressure in an automobile tire increases on a hot day. This can be explained using Gay-Lussac's Law that states that the pressure of a gas is directly proportional to the temperature if the volume remains constant. As the temperature increases, the average kinetic energy of the gas molecules increases, causing them to hit the walls of the tire more frequently, resulting in an increased pressure.
02

Understanding Phenomena (b)

In case (b), the 'popping' of a paper bag can be described using Boyle's Law. Boyle's Law states that the pressure of a gas is inversely proportional to the volume if the temperature remains constant. When a paper bag is popped, the volume decreases abruptly, which in turn increases the pressure rapidly. This leads to a sudden 'pop' sound as high-pressure air escapes quickly to the normal atmospheric pressure.
03

Understanding Phenomena (c)

In case (c), the expansion of a weather balloon as it rises in the air can be explained by using Charles's Law which states that the volume of a gas is directly proportional to the temperature if the pressure remains constant. As the balloon rises, the external pressure decreases. To maintain the pressure inside the balloon, the volume increases. Furthermore, the temperature in the upper atmosphere is also lower, which might cause the gas to contract. However, the dominant factor here is the reduced pressure, which leads to expansion of the balloon.
04

Understanding Phenomena (d)

In case (d), the loud noise heard when a lightbulb shatters can be explained using the principle of Boyle's Law again. When a bulb shatters, the gas inside it, which was at a higher pressure, suddenly comes in contact with the atmospheric pressure. This abrupt change causes a loud sound, similar to the popping of a paper bag.

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