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Question

The root mean square velocity of one mole of a monoatomic gas having molar mass M is Urms. The relation between average kinetic energy (E) of the gas and Urms is :

A
Urms=3E2M
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B
Urms=2E3M
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C
Urms=2EM
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D
Urms=E3M
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Solution

The correct option is C Urms=2EM
The root mean square velocity of one mole of a monoatomic gas having molar mass M is Urms. The relation between average kinetic energy (E) of the gas and Urms is Urms=2EM
The root mean square velocity of one mole of a monoatomic gas is given by the following expression.
Urms = 3RTM......(1)
The average kinetic energy (E) of the gas is given by the following expression.
E=32RT
RT=23E......(2)
Substitute (2) into (1)
Urms = 3×23EM
Urms = 2EM
Hence, the option (C) is the correct answer.

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