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  • The temperature of a gas is -50° C. To what temperature the gas should be heated so that the rms speed is increased by 3 times ?Option: 1 <img al

The temperature of a gas is -50° C. To what temperature the gas should be heated so that the rms speed is increased by 3 times ?

Option: 1

669\, ^{\circ}\, C


Option: 2

3295\, ^{\circ}\, C


Option: 3

3097K


Option: 4

223\, K


Answers (1)

best_answer

\begin{aligned} & \mathrm{v}_{\mathrm{rms}} \propto \sqrt{\mathrm{T}} \end{aligned}

let initial speed is v As speed is increased by 3 times so final speed becomes 4v 

\begin{aligned} \frac{\mathrm{V}_2}{\mathrm{~V}_1} & =\sqrt{\frac{\mathrm{T}_2}{\mathrm{~T}_1}} \\ \mathrm{~V}_2 & =4 \mathrm{~V}_1 \\ \mathrm{~T}_2 & =3568 \mathrm{~K} \end{aligned} \\\\or \, 3295^{\circ} \mathrm{C}

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