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RMS and KE Expressions

At what tempe...

Question

At what temperature (in Kelvin) will the particles in a sample of helium gas have an rms speed of 1.0 km/s ?

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Solution

From Maxwell's speed distribution, the RMS speed of a gas is given by the formula

$v_{r m s} = \sqrt{\frac{3 R T}{M}}$

Thus, as per question,

$1000 = \sqrt{\frac{3 (8.314) T}{4 \times 10^{- 3}}}$

$T = \frac{4000}{3 \times 8.314} \approx 160 K$

Answer is $160 K$

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