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623_Physics ProblemsTechnical Physics

# 623_Physics ProblemsTechnical Physics - Chapter 21 P21.60(a...

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Chapter 21 625 P21.60 (a) The speed of sound is v B = ρ where B V dP dV = − . According to Problem 59, in an adiabatic process, this is B P = = 1 2 κ γ . Also, ρ = = = = m V nM V nRT M V RT PM RT s a f a f where m s is the sample mass. Then, the speed of sound in the ideal gas is v B P RT PM RT M = = F H G I K J = ρ γ γ . (b) v = = 1 40 8 314 293 0 028 9 344 . . . J mol K K kg mol m s b ga f This nearly agrees with the 343 m/s listed in Table 17.1. (c) We use k R N B A = and M mN A = : v RT M k N T mN k T m B A A B = = = γ γ γ . The most probable molecular speed is 2 k T m B , the average speed is 8 k T m B π , and the rms speed is 3 k T m B . All are somewhat larger than the speed of sound. P21.61 n m M = = = 1 20 41 5 . . kg 0.028 9 kg mol mol (a) V nRT P i i i = = × = 41 5 8 314 298 200 10 0 514 3 . . . mol J mol K K Pa m 3 a fb ga f (b) P P V V f i f i = so V V P P f i f i = F H G I K J = F H G I K J = 2 2 0 514 400 200 2 . m .06 m 3 3 e j (c) T P V nR f f f = = × = × 400 10 2 06 41 5 8 314 2 38 10 3 3 Pa
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