Chapter 12, Problem 13RQ

1. 13. It is difficult to bring the Internet to some remote parts of the world. This can be inexpensively done by installing antennas tethered to large helium balloons. To help analyze the situation, assume we have inflated a large spherical balloon. The pressure on the inside of the balloon is balanced by the elastic force exerted by the rubberized material. Since we are dealing with a gas in an enclosed space, the ideal gas law will be applicable.

   PV=nRT

   Where

P = pressure [atm]

V = volume [L]

n = quant ity of gas [moles]

R = ideal gas constant [0.08206 (atm L)/ (mol K)]

T =  temperature [K]

If the temperature increases, the balloon will expand and/or the pressure will increase to maintain the equality. As it turns out, the increase in volume is the dominant effect, so we will treat the change in pressure as negligible.

The circumference of an inflated spherical balloon is measured at various temperatures; the resulting data are shown in the following graph.

1. a. What are the units of the constant 0.33?
2. b. What are the units of the constant 23.6?
3. c. What would the temperature of the balloon be if the circumference was 162 centimeters?
4. d. If a circle with an area of 100 square centimeters is drawn on the balloon at 20 degrees Celsius, what would the area be at a temperature of 100 degrees Celsius?
5. e. If the pressure inside the balloon is 1.2 atmospheres, how many moles of gas does it contain?