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Question

The molecules of a given mass of a gas have root mean square speed of 100 ms1 at 27 C and 1 atmospheric pressure. What will be the root mean square speeds of the molecules of the gas at 127 C and 2 atmospheric pressure?


A

1503 m/s

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B

1253 m/s

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C

2003 m/s

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D

1003 m/s

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Solution

The correct option is C

2003 m/s


We know that for a given mass of gas

vrms=3RTM

where R is a gas constant , T is temperature in kelvin and M is molar mass of the gas. Clearly for a given gas, vrmsT as R, M are constants.

(vrms)1(vrms)2 = T1T2
Given (vrms)1=100 m/s

T1 = 27 + 273 = 300 K

T2 = 127 + 273 = 400 K

100(vrms)2=300400=32

(vrms)2=2×1003=2003 m/s


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