RMS velocity of an ideal gas at $27^{o} C$ is $500 m / s$ , Temperature is increased four times, RMS velocity will become.

1000 m / s

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560 m / s

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2000 m / s

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None of these

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Solution

The correct option is A $1000 m / s$
$V_{r m s} = \sqrt{\frac{3 R T}{M}} = 500$ $m / s$
$V_{r m s}^{'} = \sqrt{\frac{3 R T^{'}}{M}} = \sqrt{\frac{3 R (4 T)}{M}}$
$V_{r m s}^{'} = 2 \sqrt{\frac{3 R T}{M}} = 2 V_{r m s} = 1000$ $m / s$

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RMS velocity of an ideal gas at 27oC is 500m/s, Temperature is increased four times, RMS velocity will become.

The correct option is A 1000m/sVrms=√3RTM=500 m/sV′rms=√3RT′M=√3R(4T)MV′rms=2√3RTM=2Vrms=1000 m/s

RMS velocity of an ideal gas at $27^{o} C$ is $500 m / s$ , Temperature is increased four times, RMS velocity will become.

The correct option is A $1000 m / s$
$V_{r m s} = \sqrt{\frac{3 R T}{M}} = 500$ $m / s$
$V_{r m s}^{'} = \sqrt{\frac{3 R T^{'}}{M}} = \sqrt{\frac{3 R (4 T)}{M}}$
$V_{r m s}^{'} = 2 \sqrt{\frac{3 R T}{M}} = 2 V_{r m s} = 1000$ $m / s$