Qn5. Counting Canaries Italian style: Italians love birds, many homes have these happy songsters called caries, in little cages, and to supply them is a big business. Tunisian Songbirds, Inc., is a major supplier of canaries for Southern Italy, and every Wednesday a large truck carrying these chirpy feathered creatures is loaded aboard the midweek Tunis to Naples ferry. The truck's bird container is 2.4 m wide, 3.5 m high, solid on the sides and bottom, open at the top except for a restraining screen, and has a total open volume available for birds of 36 m. On arrival at Naples a tax of 10 lira/bird is to be charged by the customs agent, but how to determine the amount to be assessed? Since counting these thousands of birds one by one would be impractical the Italians use the following ingenious method. TUNISIAN SONGBIRDS GOOD BIRDS FOR A SONG screen on top P = 102875 Pa P. 103316 Pa The customs agent sets up his pressure gauges, then loudly bangs the side of the van with a hammer. This scares the birds off their perches up into the air. Then he carefully records the pressure both at the bottom and at the top of the inside of the van. If the pressure at the bottom is 104,316 Pa, the pressure at the top is 102,875 Pa, and the temperature is 25C, how much tax should the customs agent levy? Additional data: Juvenile canaries have a mass of 15 gm and a density estimated to be 500 kg/m. [Levenspiel]