Question

A bag of potato chips is packed and sealed in Los Angeles, California, and then shipped to Lake Tahoe, Nevada, during ski season. It is noticed that the volume of the bag of potato chips has increased upon its arrival in Lake Tahoe. What external conditions would most likely cause the volume increase?

Short answer

The most likely external condition causing the volume increase of the bag of potato chips when transported from Los Angeles to Lake Tahoe is the change in atmospheric pressure due to the difference in altitude between the two locations. As Lake Tahoe is at a higher altitude, the pressure is lower, which leads to an increase in volume according to the Ideal Gas Law, assuming the amount of gas inside the sealed bag remains constant.

Step-by-step solution

Identifying relevant gas laws

We will consider the Ideal Gas Law to determine the changes in external factors that contribute to the increase in volume. The Ideal Gas Law is given by the equation \(PV = nRT\), where P is pressure, V is volume, n is the number of moles of the gas, R is the gas constant, and T is temperature in Kelvin. For an ideal gas, the product of pressure and volume (PV) is constant, if the amount of gas and its temperature remain the same. As we are dealing with a sealed bag of chips, the number of gas moles in this specific bag remains constant. Therefore, we have to analyze the conditions regarding pressure and temperature.

Changes in pressure

The atmospheric pressure typically decreases with increasing altitude. Given that Lake Tahoe has a higher altitude than Los Angeles, the pressure at Lake Tahoe is lower than in Los Angeles. Since the bag is sealed and the amount of gas inside remains constant, using Ideal Gas Law, we can see that if pressure decreases, the volume should increase.

Changes in temperature

Temperature changes can also impact the volume of a gas inside a container, according to the Ideal Gas Law. As we move from Los Angeles to Lake Tahoe during ski season, we would expect the temperature to be colder in Lake Tahoe than in Los Angeles. However, a decrease in temperature would typically lead to a decrease in volume. In this particular scenario, we are looking for factors causing an increase in volume, so the change in temperature may not be the primary reason for the observed volume increase.

Conclusion

The most likely external condition that causes the volume increase of the bag of potato chips when transported from Los Angeles to Lake Tahoe is the change in pressure due to the difference in altitude between the two locations. As Lake Tahoe is at a higher altitude, the atmospheric pressure is lower, which leads to an increase in volume according to the Ideal Gas Law, assuming the amount of gas inside the sealed bag remains constant.