560 TemperatureP19.44(a)Initially the air in the bell satisfies PVnRTi0bell=orPAnRTi0250. maf=(1)When the bell is lowered, the air in the bell satisfiesPxAnRTfbellm.−=(2)where xis the height the water rises in the bell. Also, the pressure in the bell, once it islowered, is equal to the sea water pressure at the depth of the water level in the bell.PPgxPgbellm m=+−≈+0082 382 3ρρ..afaf(3)The approximation is good, as x<.m. Substituting (3) into (2) and substituting nRfrom(1) into (2),PgxAPVTTfi82 32 50+−=ρmbellaf.Using P051101310==×atmPa.and =×1025 103kgm3xTTgPxf=−+FHGIKJLNMMOQPP+××FHGGIKJJLNMMMOQPPP=−−1182 31277 1519808231013 102241351.......mmmK293.15 Kkg mm smNmm322afafejej(b)If the water in the bell is to be expelled, the air pressure in the bell must be raised to thewater pressure at the bottom of the bell. That is,
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