First slide

Rms speed

Question

Ifat N.T.P., velocity of sound in a gas is 1150 m/s, then the r.m.s. velocity of gas molecules at N.T.P. is : (Given R = 8.3 J/mol K and C_P = 4.8 cal/mol K)

Moderate

A

1600 m/s
B

1532.19 m/s
C

160 m/s
D

16 m/s

Solution

Here, $R = \frac{8 \cdot 3}{4 \cdot 2} cal / g mol K$
$C_{v} = C_{p} - R = (4.8 - \frac{8 \cdot 3}{4 \cdot 2}) = 2 \cdot 824 c a l / m o l K ∴ γ = \frac{C_{p}}{C_{V}} = \frac{4 \cdot 8}{2 \cdot 824} = 1 \cdot 69 So, v_{rms} = \sqrt{(\frac{3}{γ})} v_{sound} = 1532 \cdot 19 m / s$

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