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Chapter 5: Problem 24

As weather balloons rise from the earth's surface, the pressure of the atmosphere becomes less, tending to cause the volume of the balloons to expand. However, the temperature is much lower in the upper atmosphere than at sea level. Would this temperature effect tend to make such a balloon expand or contract? Weather balloons do, in fact, expand as they rise. What does this tell you?

Short Answer

Expert verified
As a weather balloon rises in the atmosphere, the pressure decreases, causing the volume to expand according to the Ideal Gas Law (\(PV = nRT\)). However, the decrease in temperature should cause the volume to contract. Since weather balloons do expand as they rise, it indicates that the pressure decrease is more dominant than the temperature decrease. As a result, the expansion of the volume primarily happens due to the decreasing pressure, and the temperature effect is not enough to prevent this expansion.

Step by step solution

01

Understand the Ideal Gas Law

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 gas, R is the ideal gas constant, and T is temperature in Kelvin. The relationship between pressure, volume, and temperature can help us understand how the volume of the weather balloon is affected by changing pressure and temperature.
02

Analyze the effect of pressure

As the weather balloon rises from the Earth's surface, the pressure of the atmosphere decreases. According to the Ideal Gas Law, when the pressure decreases and other variables remain constant, the volume of the gas increases. Thus, the decrease in pressure should cause the weather balloon to expand.
03

Analyze the effect of temperature

The temperature in the upper atmosphere is much lower than at sea level. To analyze the effect of temperature on the volume of the balloon, we have to consider the Ideal Gas Law again. When the temperature decreases and other variables remain constant, the volume of the gas should decrease. So, the decrease in temperature should cause the weather balloon to contract.
04

Balancing pressure and temperature effects

We have found that the decrease in pressure should cause the balloon to expand, while the decrease in temperature should cause the balloon to contract. Since weather balloons do expand as they rise, it means that the effect of the pressure decrease is more dominant than the effect of temperature decrease. Thus, as the balloon rises, its volume expands primarily due to decreasing pressure, and the temperature effect is not enough to prevent this expansion.

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