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Question: The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K, the rms velocity of t...

The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K, the rms velocity of the gas molecules is vrms, then at 480 K, it becomes

A

4 vrms

B

2 vrms

C

νrms2\frac{\nu_{\text{rms}}}{2}

D

νrms4\frac{\nu_{\text{rms}}}{4}

Answer

4 vrms

Explanation

Solution

Vrms2Vrms1=T2T1=480120\frac{V_{rms_{2}}}{V_{rms_{1}}} = \sqrt{\frac{T_{2}}{T_{1}}} = \sqrt{\frac{480}{120}}

Vrms=2(Vrms1)V_{rms} = 2(V_{rms1})