558_Physics ProblemsTechnical Physics

# 558_Physics ProblemsTechnical Physics - 560 P19.44...

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560 Temperature P19.44 (a) Initially the air in the bell satisfies PV nRT i 0b e l l = or PA n R T i 0 250 . m af = (1) When the bell is lowered, the air in the bell satisfies Px A n R T f bell m . −= (2) where x is the height the water rises in the bell. Also, the pressure in the bell, once it is lowered, is equal to the sea water pressure at the depth of the water level in the bell. PP g x P g bell m m =+ −≈+ 00 82 3 82 3 ρρ .. a f a f (3) The approximation is good, as x < . m. Substituting (3) into (2) and substituting nR from (1) into (2), Pg x A P V T T f i 82 3 2 50 +− = ρ m bell a f . Using P 0 5 11 0 1 3 1 0 == × atm Pa . and 1025 10 3 k g m 3 x T T g P x f =− + F H G I K J L N M M O Q P P + × × F H G G I K J J L N M M M O Q P P P = 1 1 82 3 1 277 15 1 980 823 1013 10 224 1 3 5 1 . . . . . . . m m m K 293.15 K kg m m s m Nm m 32 2 a f a f ej e j (b) If the water in the bell is to be expelled, the air pressure in the bell must be raised to the water pressure at the bottom of the bell. That is,
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