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The velocities of sound in an ideal gas at temperature T1, and T2, K are found to be V1, and V2, respectively. If the root mean square speeds of the same gas at the same temperatures. T1 and T2, are v1, and v2, respectively, then

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a

v2=v1V2/V1

b

v2=v1V1/V2

c

V2=V1V2/V1

d

V2=V1V1/V2

answer is A.

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Detailed Solution

we know that V=γPρ and PV=RTV1V2=γRT1/M1/2γRT2/M1/2=T1T21/2 Further rv1v2=3RT1/M1/23RT2/M1/2=T1T21/2 V1V2=v1v2  or  v2=v1V2V1
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The velocities of sound in an ideal gas at temperature T1, and T2, K are found to be V1, and V2, respectively. If the root mean square speeds of the same gas at the same temperatures. T1 and T2, are v1, and v2, respectively, then