Calculate the change in air pressure you will experience if you climb a 1000-m mountain, assuming that the temperature and air density do not change over this distance and that they were 22°C and 1.2 kg/m³, respectively, at the bottom of the mountain.
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- On a nice winter day at the South Pole, the temperature rises to -55°F. What is the approximate temperature in degrees Celsius? °℃ Need Help? Read ItOne easy way to reduce heating (and cooling) costs is to add extra insulation in the attic of a house. Suppose the house already had 15 cm of fiberglass insulation in the attic and in all the exterior surfaces. If you added an extra 8.0 cm of fiberglass to the attic, then by what percentage would the heating cost of the house drop? Take the single story house to be of dimensions 10 m by 15 m by 3.0 m. Ignore air infiltration and heat loss through windows and doors.People that live at high altitudes often notice that sealed bags of food are puffed up because the air inside has expanded since they were sealed at a lower altitude. In one example, a bag of potato chips was packed at a pressure of 1.00atm and a temperature of 20.5 degrees celcius. The bag was then transported to Santa Fe. The sealed bag of potato chips then finds its way to a summer picnic where the temperature is 31.6 degrees celcius, and the volume of air in the bag has increased to 1.4 times its original value. At the picnic in Santa Fe, what is the pressue, in atmospheres, of the air in the bag?
- The summit of a mountain is 3240 m higher than a point in the foothills. Assume that the atmospheric lapse rate in this area is the same as the global average of -6.5°C/km. What is the temperature of the summit when eager hikers depart from the foothill location at a temperature of 28°C?Soon after the Earth formed, heat released by the decay of radioactive elements raised the average internal temperature from 300 to 3000 K, at about which value it remains today. Assuming an average coefficient of volume expansion of 3.0 x 10-5 K -1 , by how much has the radius of the Earth increased since its formation? (Let r = 6400km be the present radius of the Earth.)The density of water that is at 0°C is very nearly 1000 kg/m³ (it is actually 999.84 kg/m³), whereas the density of ice that is at 0°C is 917 kg/m³. Calculate the pressure necessary to keep 4.6 m³ of water from expanding when it freezes, neglecting the effect such a large pressure would have on the freezing temperature. (This problem gives you only an indication of how large the forces associated with freezing water might be.) The bulk modulus of ice is 2.20 x 109 N/m². How is density related to the mass and volume of a substance? How is the change in volume due to expansion or contraction related to the thermal stress? N/m²
- Suppose you have a large hot air balloon, open at the bottom but filled with air that is heated to 50 °C while the outside air is 10 °C. What can you say about the air inside the balloon and how much it can lift? The density of air is surprisingly high: 1.23 kg/m3, an average hot air balloon has a volume of 3000 m3 , and the acceleration of gravity is 9.8 m/s2. The density is higher by the factor (273 + 50)/(273+10) = 1.14 and therefore will not have a buoyant force and will not lift off the ground with any load. The density is lower by the factor (273 + 10)/(273+50) = 0.88 and therefore will have a buoyant force of 0.88 times the weight of the air it replaced, or about 32,000 N. The density is lower by the factor (273 + 10)/(273+50) = 0.88 and therefore will have a buoyant force of 0.12 times the weight of the air it replaced, or about 4300 N. The density is the same but the pressure of the hot air is higher by (273 + 50)/(273+10) =…(a) Calculate the change in air pressure you’ll experience if you climb a 1000 m mountain, assuming for simplicity that the temperature and air density do not change over this distance and that they were 22C and 1.2 kg/m3, respectively, at the bottom of the mountain. (Note: The result of Example 18.4 doesn’t apply, since the expression derived in that example accounts for the variation of air density with altitude and we are told to ignore that here.) (b) If you took a 0.50 L breath at the foot of the mountain and managed to hold it until you reached the top, what would be the volume of this breath when you exhaled it there?In the summer of 1958 in St. Petersburg, Florida, a new sidewalk was poured near the childhood home of one of the authors. No expansion joints were supplied, and by mid-July the sidewalk had been completely destroyed by thermal expansion and had to be replaced, this time with the important addition of expansion joints! This event is modeled here. A slab of concrete 4.00 cm thick, 1.00 m long, and 1.00 m wide is poured for a sidewalk at an ambient temperature of 25.0°C and allowed to set. The slab is exposed to direct sunlight and placed in a series of such slabs without proper expansion joints, so linear expansion is prevented. (a) Using the linear expansion equation (Eq. 10.4), eliminate Δ L from the equation for compressive stress and strain (Eq. 9.3). (b) Use the expression found in part (a) to eliminate Δ T from Equation 11.3, obtaining a symbolic equation for thermal energy transfer Q. (c) Compute the mass of the concrete slab given that its density is 2.40 × 103 kg/m3. (d)…