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Chapter 8: 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
In conclusion, while the temperature decrease in the upper atmosphere would tend to make the weather balloon contract, the dominating factor causing the balloon to expand is the decrease in atmospheric pressure. The fact that weather balloons expand as they rise indicates that the pressure decrease at higher altitudes has a more significant impact on the balloon's volume than the temperature decrease.

Step by step solution

01

Understand the opposing effects of the two factors involved in this problem: pressure and temperature on the volume of the weather balloon as it rises from the surface

At higher altitudes, atmospheric pressure tends to decrease, leading to an increase in the volume of the weather balloon. However, the temperature at those altitudes tends to be lower than at sea level, which would generally make the balloon contract. We will now analyze each factor separately to understand their effects on the volume of the weather balloon.
02

Apply the ideal gas law to analyze the effect of pressure on the volume of the weather balloon

The ideal gas law can be expressed as: \[PV = nRT\] Where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin. As the weather balloon rises and the atmospheric pressure decreases, we can see from the ideal gas law that the volume should increase, assuming the temperature and the number of moles of gas inside the balloon remain constant.
03

Apply the ideal gas law to analyze the effect of temperature on the volume of the weather balloon

With the ideal gas law as our basis, we can now evaluate the impact of a decrease in temperature on the volume of the weather balloon. If the pressure and the number of moles of gas inside the balloon remain constant, we can observe that if the temperature decreases, the volume should also decrease.
04

Determine the dominating effect on the weather balloon's volume

In this case, we know that weather balloons expand as they rise. This indicates that the effect of pressure decrease must be greater than the effect of temperature decrease, which means that the net decrease in pressure at higher altitudes is substantial enough to cause an increase in volume despite the decrease in temperature. In conclusion, while the temperature decrease in the upper atmosphere would tend to make the weather balloon contract, the dominating factor causing the balloon to expand is the decrease in atmospheric pressure. This tells us that the pressure decrease at higher altitudes has a more significant impact on the balloon's volume than the temperature decrease.

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Most popular questions from this chapter

Metallic molybdenum can be produced from the mineral moIybdenite, MoS \(_{2}\). The mineral is first oxidized in air to molybdenum trioxide and sulfur dioxide. Molybdenum trioxide is then reduced to metallic molybdenum using hydrogen gas. The balanced equations are $$\begin{array}{l}\operatorname{MoS}_{2}(s)+\frac{7}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{MoO}_{3}(s)+2 \mathrm{SO}_{2}(g) \\\\\mathrm{MoO}_{3}(s)+3 \mathrm{H}_{2}(g) \longrightarrow \mathrm{Mo}(s)+3 \mathrm{H}_{2} \mathrm{O}(l)\end{array}$$ Calculate the volumes of air and hydrogen gas at \(17^{\circ} \mathrm{C}\) and \(1.00\) atm that are necessary to produce \(1.00 \times 10^{3} \mathrm{kg}\) pure molybdenum from MoS \(_{2}\). Assume air contains \(21 \%\) oxygen by volume, and assume \(100 \%\) yield for each reaction.

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