Activity 1: Graphing Scuba divers must learn about pressure under water. At the water’s surface, air exerts 1 atmosphere (atm) of pressure. Under water, the pressure increases. The pressure P (atm) varies with depth d (ft) according to the equation . Boyle’s law (PV = k) states that the volume V of air varies inversely with the pressure P. If you hold your breath, the volume of air in your lungs increases as you ascend. If you have 4 qt of air in your lungs at a depth of 66 ft (P = 3 atm), the air will expand to 6 qt when you reach 33 ft, where P = 2 atm. Using the data in the example above, make a table and graph to show how the volume of air in your lungs varies with depth. Make a table and graph to show how the volume of air in your lungs varies with pressure.
Activity 2: Writing In Activity 1, you found that the volume of air in a diver’s lungs could more than double as the diver resurfaces. This expansion can cause the membranes of the lungs to rupture. Divers must learn to exhale properly while ascending. If you fill your lungs with 4 qt of air at a depth of 66 ft, how many quarts of air will you need to exhale during your ascent to still have 4 qt of air in your lungs when you reach the surface? Write an explanation of why beginning divers are told, “Don’t hold your breath!” Refer to your tables and graphs.
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Activity 3: Solving A popular size of scuba-diving tank is 71.2 ft3 because this is the volume that the compressed air inside the tank would occupy at a normal surface pressure of 1 atm. The air in the tank is at a pressure of about 2250 lb/in.2, so the tank itself can have a volume much less than 71.2 ft3. How large does the tank need to be to hold 71.2 ft3? (Hint: Use Boyle’s Law: PV = k. Remember that 1 atm = 14.7 lb/in.2.)
Activity 4: Solving The rate at which a scuba diver uses air in the tank depends on many factors, such as the diver’s age and lung capacity. Another important factor is the depth of the dive. A scuba diver continues to breathe normally while descending. Every time the diver inhales, the tank delivers enough air to inflate the diver’s lungs. This means that the amount of air delivered by the tank must increase with the depth in order to withstand the increasing pressure. At greater depths, the diver uses the air in the tank more quickly. The amount of time the air will last is inversely proportional to the pressure at the depth of the dive. Suppose a tank has enough air to last 60 min at the surface. How long will it last at a depth of 99 ft? (The pressure is 4 atm, or 4 times as great.) Make a table showing how long the air will last at 0 ft, 20 ft, 33 ft, 40 ft, 50 ft, 66 ft, and 99 ft.
Mathematics homework help