Question

Calculate the volume of air within a typical bicycle tire (or, if you like, choose an atypical tire size that you prefer). This calculation does not need to be precise: A reasonable approximation would be the volume of a cylinder with the radius of the inner tube and the length of its circumference.

(b) Calculate the number of moles of air molecules in the inflated tire. For this calculation, it is reasonable to treat the air as an ideal gas and use the gas constant with units of atmospheres for pressure and liters for volume: R = 0.08206 L · atm · K −1mol−1 Assume that the temperature is 300 K, and be sure to indicate the final pressure that you are assuming. What is the initial volume of the air at atmospheric pressure?

(c) Calculate the entropy change, at 300 K, for compressing the air from 1 atm to the final pressure.

(d) How would you go about filling the tire with the minimum amount of work? What conditions would you maintain during this process? What is the minimum amount of work required?

(e) If you have much experience with this activity, you probably know that the temperature of the air is likely to increase as you fill the tire. Why does the temperature increase? How would you expect the temperature increase to affect the amount of work that you have to do? (f) Suppose that you have just eaten a candy bar. How many tires must you pump up to work off the nutritional energy of the candy bar, assuming that 10% of the candy bar calories are converted to work (and the rest to metabolic heat)? Also assume that the temperature of the air remains constant and that you use the minimum amount of work to pump up each tire. Be careful: nutritional information is usually reported in “big C” calories, which is the amount of energy required to raise the temperature of 1 Kg of water by 1 ◦C, not 1 g.