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Gases: Pressure


Pressure and the Barometer

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Problem : Blaise decides to build a barometer. He can't find any mercury in his workshop and decides to use water instead. Assume that the density of water is 1.00×103 kg/m3 . If the atmospheric pressure is 7.60×102 torr, how tall must his barometer be in order to obtain an accurate reading?

First, convert the atmospheric pressure to Pascals. 7.60×102 torr = 101, 325 Pa . Now that all the variables are in SI units, rearrange P = ghρ to P/() = h and plug the variables into the equation.

= = 10.3 m    

Thus Blaise's barometer must be taller than 10.3 meters. A comparable mercury barometer would be 0.76 m tall.

Problem :

In a fit of inspiration and hot air, you have blown the world's largest balloon. Your two cousins, Bongo the 300 lb. gorilla and Jeeves the 70 lb. weakling, both want to climb to the top of your balloon. When Bongo goes, he goes in style. He wants to lay down on his 1 m by 5 m air bed at the summit. Jeeves proposes to bounce on the top of the balloon on his pogo stick, whose head has an area of 0.001 m2 . Assume that the masses of the bed and pogo stick are negligible, and that their occupants' weights are evenly distributed upon them.

You know that your balloon can sustain 200 more kPa of pressure on its surface before it pops. Assuming both can make it to the top without damaging the balloon (or themselves), which cousin(s) should you allow to climb?

P = F/A , so the first thing we need to do is convert everything to the appropriate units. Let's use SI units. 1 lb = 0.454 kg, and F = (mass)×(9.8 m/s2) , so Bongo and Jeeves exert forces of 1330 and 311 Newtons, respectively. P = F/A , so Bongo has a pressure of P Bongo = = 270 Pa. Jeeves exerts a pressure of P Jeeves = (311 N)×(0.001 m2) = 310 kPa. You should allow Bongo on, but not Jeeves.

Problem : After an interdimensional mishap, Blaise finds himself on a strange planet with nothing but an empty barometer and a jar of alien liquid. After working with barometers for many years, Blaise has developed a keen sense of pressure. He reckons that the atmospheric pressure is 1.4 atmospheres. The label on the jar claims that the density of the liquid is 1.0×105 . He pours the liquid into his barometer, and finds that the atmosphere supports a column 0.072 m tall. What is the gravitational acceleration g on this planet?

We can rearrange the barometer equation to solve for g :

= g    

Let's stick with SI units to keep everything consistent. 1 atm = 1.013×105 Pa, so P is 142,000 Pa. Plugging in h and ρ , we find that g = 20  .

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