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Question

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The relation known as the barometric formula is useful for determining the approximate change in pressure due to altitude. The formula, derived from the ideal gas law is: P= P0e^(-gMh/RT), where P is the pressure at height h, P0 is the pressure at sea level, g is the acceleration due to gravity (9.8 m/s) M is the average molar mass of air (29.0g/mol) and R is the gas constant. If 4.0 g of air are put into a balloon at sea level, then that balloon is taken to an altitude of 3.00 x 10^3 m, what is the change in volume? Assume a constant temperature of 20C

Answer 1

If the temperature is constant, the the gas law states that P*V is constant. Find Pa/P0 (pressure at altitude/sea level) from the barometric formula Pa/P0 = e^(-gmh/RT) with h = 3*10^m. Then Va = V0*P0/Pa, where V0 = balloon volume at sea level, and Va = balloon volume at 3*10^3m