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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
Despite the decrease in temperature in the upper atmosphere, weather balloons expand as they rise due to the decrease in atmospheric pressure. This indicates that the pressure effect, which causes the volume to increase, outweighs the temperature effect, which would cause the volume to decrease. The combined effect of decreasing pressure and temperature results in the overall expansion of the weather balloon.

Step by step solution

01

Understand the gas laws

The behavior of gases under different conditions of temperature and pressure is described by the gas laws. Two main gas laws that are relevant to this exercise are Boyle's Law and Charles's Law. Boyle's law states that at a constant temperature, the pressure and volume of a gas are inversely proportional. \(P_1V_1 = P_2V_2\) Charles's law states that at a constant pressure, the volume of a gas is directly proportional to its temperature in kelvins. \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\) We can combine these two laws into a single equation, known as the Combined Gas Law. \(\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}\)
02

Analyze the expansion of the balloon under changing pressure

As the weather balloon rises, the atmospheric pressure decreases. As per Boyle's law, since the pressure decreases, the volume of the balloon must increase if the temperature remains constant.
03

Analyze the expansion of the balloon under changing temperature

As the weather balloon rises, the temperature also decreases. According to Charles's law, as the temperature of the gas inside the balloon decreases, its volume should decrease when the pressure remains constant.
04

Evaluating the combined effect of atmospheric pressure and temperature

As the balloon rises, both temperature and pressure decrease. However, the combined effect of both pressure and temperature on the volume depends on which factor has a greater influence. We know that weather balloons expand as they rise, which indicates that the reduction of pressure (leading to an increase in volume) outweighs the reduction in temperature (leading to a decrease in volume). The overall effect is expansion.
05

Conclusion

Despite the decrease in temperature in the upper atmosphere, which would tend to cause the balloon to contract, weather balloons do, in fact, expand as they rise due to the decrease in atmospheric pressure.

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Most popular questions from this chapter

Atmospheric scientists often use mixing ratios to express the concentrations of trace compounds in air. Mixing ratios are often expressed as ppmv (parts per million volume): ppmv of \(X=\frac{\text { vol of } X \text { at STP }}{\text { total vol of air at STP }} \times 10^{6}\) On a certain November day, the concentration of carbon monoxide in the air in downtown Denver, Colorado, reached \(3.0 \times 10^{2}\) ppmv. The atmospheric pressure at that time was 628 torr and the temperature was \(0^{\circ} \mathrm{C}\). a. What was the partial pressure of \(\mathrm{CO}\) ? b. What was the concentration of \(\mathrm{CO}\) in molecules per cubic meter? c. What was the concentration of \(\mathrm{CO}\) in molecules per cubic centimeter?

A 20.0-L stainless steel container at \(25^{\circ} \mathrm{C}\) was charged with \(2.00\) atm of hydrogen gas and \(3.00\) atm of oxygen gas. A spark ignited the mixture, producing water. What is the pressure in the tank at \(25^{\circ} \mathrm{C} ?\) If the exact same experiment were performed, but the temperature was \(125^{\circ} \mathrm{C}\) instead of \(25^{\circ} \mathrm{C}\), what would be the pressure in the tank?

In Example \(5.11\) of the text, the molar volume of \(\mathrm{N}_{2}(g)\) at STP is given as \(22.42 \mathrm{~L} / \mathrm{mol} \mathrm{N}_{2}\). How is this number calculated? How does the molar volume of \(\mathrm{He}(g)\) at STP compare to the molar volume of \(\mathrm{N}_{2}(\mathrm{~g})\) at STP (assuming ideal gas behavior)? Is the molar volume of \(\mathrm{N}_{2}(g)\) at \(1.000 \mathrm{~atm}\) and \(25.0^{\circ} \mathrm{C}\) equal to, less than, or greater than \(22.42 \mathrm{~L} / \mathrm{mol}\) ? Explain. Is the molar volume of \(\mathrm{N}_{2}(g)\) collected over water at a total pressure of \(1.000\) atm and \(0.0^{\circ} \mathrm{C}\) equal to, less than, or greater than \(22.42\) \(\mathrm{L} / \mathrm{mol}\) ? Explain.

Cyclopropane, a gas that when mixed with oxygen is used as a general anesthetic, is composed of \(85.7 \% \mathrm{C}\) and \(14.3 \% \mathrm{H}\) by mass. If the density of cyclopropane is \(1.88 \mathrm{~g} / \mathrm{L}\) at STP, what is the molecular formula of cyclopropane?

Natural gas is a mixture of hydrocarbons, primarily methane \(\left(\mathrm{CH}_{4}\right)\) and ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\). A typical mixture might have \(\chi_{\text {methane }}=\) \(0.915\) and \(\chi_{\text {ethane }}=0.085\). What are the partial pressures of the two gases in a \(15.00\) - \(\mathrm{L}\) container of natural gas at \(20 .{ }^{\circ} \mathrm{C}\) and \(1.44\) atm? Assuming complete combustion of both gases in the natural gas sample, what is the total mass of water formed?
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