planeparatm consider an isothermal atmosphere on the surface of a star, which has a very small height and is in hydrostatic equilibrium. this means that the atmosphere can be treated as plane parallel: in the equation of hydrostatic equilibrium, dp/dr can be replaced by dp/dz, where z is the height above the surface of the star. moreover, the surface gravity, g, is constant over the height of the atmosphere (a) under these assumptions, start with the equation of hydrostatic equilibrium and derive a differential equation for the density of this atmosphere (b) solve this equation to obtain the density as a function of height above the surface of the star (c) in your solution, identify the "scale height," i. e. a quantity with dimensions of length, which represents the height over which the density of the atmosphere changes appre- ciably. (d) calculate the pressure at the base of the atmosphere. (e) using the ideal gas equation of state and your solution for the density structure of the atmosphere from part (b), compute the pressure at the surface of the star. compare your answer to what you found in part (d). what do you conclude from this exercise?

Amajor impediment to wide acceptance of electric vehicles even on the part of people who use their cars almost exclusively for commuting is the inability to use their electric vehicles for occasional extended trips. in an attempt to make purchasing electric vehicles more attractive to commuters, one electric vehicle producer is planning to offer customers three days free rental of a conventional car for every 1,000 miles that they drive their electric vehicle. which of the following, if true, most threatens the plan's prospects for success? (a) many electric vehicles that are used for commercial purposes are not needed for extended trips. (b) because a majority of commuters drive at least 100 miles a week, the cost to the producer of making good the offer would add considerably to the already high price of electric vehicles. (c) the relatively long time it takes to recharge the battery of an electric vehicle can easily be fitted into the regular patterns of car use characteristic of commuters. (d) although electric vehicles are essentially emission-free in actual use, generating the electricity necessary for charging an electric vehicle's battery can burden the environment. (e) some family vehicles are used primarily not for commuting but for making short local trips, such as to do errands.