Kinetic Theory of Gases

Chemistry Level 2

The rms speed of 8 g of Helium is 300 m/s. Then the total kinetic energy of He gas is

240 J 480 J 360 J 120 J

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1 solution

Md Zuhair
Oct 3, 2017

We know v r m s = 3 R T M v_{rms} = \sqrt{\dfrac{3RT}{M}}

300 = 3 R T 4 × 1 0 3 \implies 300 = \sqrt{\dfrac{3RT}{4 \times 10^{-3}}}

30 0 2 = 3 R T 4 × 1 0 3 \implies 300^2 = \dfrac{3RT}{4 \times 10^{-3}}

R T = 120 \implies RT = 120 .

Now For each direction, that is x,y,z axis, Energy is n R T 2 \dfrac{nRT}{2}

So By Law Of Equipartition of energy,

E k = 3 n R T 2 E_{k} = \dfrac{3nRT}{2}

So Putting value of n = 8 / 4 = 2 n=8/4 = 2 and R T = 12 RT=12

E k = 360 k J E_{k}=360 kJ [ANS]

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