Question
Please Help
Estimate the total volume of our classroom, in m3. Estimate the total number of molecules in our classroom. (To simplify: Assume it's all nitrogen gas!) Estimate the number of moles of nitrogen gas in our classroom. What's the total mass of nitrogen in our classroom. Obtain the nitrogen density from your values above. Compare to the actual density of nitrogen at atmospheric pressure (1 atm): 1.25 grams/Liter. Here is a standard tire gauge, shown as a cross-section (from howstuffworks.com) There are two environments, separated by a movable piston. To the right of the piston is a spring and rod, both open to the room atmospheric pressure. To the left of the piston is open to the tire chamber, so will be at the tire's pressure when connected. Assume that when the gauge is not connected, the gauge reads zero. (This is called a differential pressure gauge, and is the typical gauge). Here are the specifications of the gauge: Piston area = 7.9times10-5 m2. Spring constant of the spring = 9.24times102 N/m. Assume your garage is at 1atm. NOW you connect the gauge to your motorcycle and the piston forces the rod out a distance of 2.0cm (0.020 meters). Obtain the differential pressure in the tire, in psi. (The differential pressure is the amount of pressure the tire is above 1atm.) Note: 1 psi = 6.894times103 Pa. Obtain the actual pressure in the tire. That is, include the atmospheric pressure.
Explanation / Answer
part1) volume=100m^3; molecules=9000Na; moles=9000; mass=9000*14=112000; rho=mass/volume=1.26g/liter slightly more than actual densuty
part2,a)piston forces=k*x=9.24*100*0.02;=18.48N;
differential pressure=F/A=18.48/7.9*10^5=233924.051Pa;(233924.051/6.894/1000=33.93psi)
part2,b)actual pressure=differential pressure+atm=33.93+14.69=48.62psi