1 Relate hot-air balloon flights to Charles' law The history of hot-air balloons is closely related to Jacques Charles. His studies made it possible to calculate the volume increase that a gas experiences when it is heated to a certain temperature, keeping it at atmospheric pressure. How is the flight of a hot-air balloon controlled? • Some hot-air balloons are made of a flexible material. In some balloons a gas that is lighter than air is used. This was hydrogen at first, but today it is helium. • When heated, the temperature of the gas increases and it expands. As the hot-air balloon and its gas are in the atmosphere, the process is performed at a constant pressure (atmospheric pressure). Volume and temperature are directly proportional (Charles' law). • The balloon, with the hot gas, is less dense than air, and can ascend and keep itself in flight. • To descend, the gas is no longer heated. The temperature decreases and, with it, the volume in the same proportion. • The density of the air in the balloon gradually increases and the balloon can descend. SOLVED PROBLEM 4 In a kitchen, where the temperature is 30 °C, there is a bottle partially filled with water. The free space of 200 mL is occupied by a gas. We put it in the fridge, where the temperature is 4 °C. What volume does the gas in the bottle occupy? If the bottle is made of soft plastic, what happens to it? 1. Write the two states of the gas with their quantities. p1 = 1 atm V1 = 200 mL T1 = 30 °C p2 = 1 atm V2 = ? T2 = 4 °C 2. Identify the law to apply. For a transformation when p = constant, apply Charles’ law. V T V T 1 1 2 2 = 3. Make V2 the subject. V T V T V T V T V T T V 1 1 2 2 1 2 2 1 2 2 1 1 = → ⋅ = ⋅ → = ⋅ 4. B efore substituting the data, write all the amounts of each quantity in the same units. The temperature must be in kelvin: T1 (K) = T1 (°C) + 273 = 30 °C + 273 = 303 K T2 (K) = T2 (°C) + 273 = 4 °C + 273 = 277 K Apply Charles’ law: V T T V 2 2 1 1 182 8 = = = ⋅ ⋅ 277 K 303 K 200 mL . mL The gas occupies a smaller volume. If the bottle is soft plastic, it will get crushed. 12 A balloon occupies a volume of 1 m3 at a temperature of 20 °C. The gas inside is heated to 100 °C. What will be its volume now if the process took place at atmospheric pressure? 13 Explain whether this is true: “When a gas experiences transformations at a constant pressure, its volume and temperature are directly proportional. That is, if its temperature goes from 20 °C to 40 °C, its volume also doubles.” A C T I V I T I E S 17
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