If a space shuttle is struck by a meteor, producing a circular hole 1.0 cm in diameter in the window, how long does it take before the pressure inside the cabin is reduced to half of its original value? Assume that the cabin of the shuttle is a cube with edges measuring 5.00 m with a constant temperature of 21 °C at 1.0 atm and that the air inside consists of uniform diatomic molecules each with a mass of 15 amu. (Hint: What fraction of the molecules are moving in the correct direction to exit through the hole, and what is their average speed? Derive an expression for the rate at which molecules exit the hole as a function of pressure, and thus of dp/dt.)
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