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Question: A flask contains \(10^{- 3}m^{3}\) gas. At a temperature, the number of molecules of oxygen are \(3....

A flask contains 10−3m310^{- 3}m^{3} gas. At a temperature, the number of molecules of oxygen are 3.0×10223.0 \times 10^{22}. The mass of an oxygen molecule is 5.3×10−265.3 \times 10^{- 26}kg and at that temperature the rms velocity of molecules is 400 m/s. The pressure in N/m2N/m^{2} of the gas in the flask is

A

8.48×1048.48 \times 10^{4}

B

2.87×1042.87 \times 10^{4}

C

25.44×10425.44 \times 10^{4}

D

12.72×10412.72 \times 10^{4}

Answer

8.48×1048.48 \times 10^{4}

Explanation

Solution

V=10−3m3V = 10^{- 3}m^{3}, N=3.0×1022N = 3.0 \times 10^{22}, m=5.3×10−26kgm = 5.3 \times 10^{- 26}kg,

vrms=400m⥂/⥂sv_{rms} = 400m ⥂ / ⥂ s

P=13mNVvrms2=13×5.3×10−26×3.0×102210−3(400)2P = \frac{1}{3}\frac{mN}{V}v_{rms}^{2} = \frac{1}{3} \times \frac{5.3 \times 10^{- 26} \times 3.0 \times 10^{22}}{10^{- 3}}(400)^{2}.=8.48×104N⥂/⥂m2= 8.48 \times 10^{4}N ⥂ / ⥂ m^{2}