Q138 / 160 · TS EAMCET 2024 (09 May Shift 2) · Physics

If the temperature of a gas is increased from $27^{\circ} \mathrm{C}$ to $159^{\circ} \mathrm{C}$, the increase in the rms speed of the gas molecules is

  • A
    $142 \%$
  • B
    $71 \%$
  • C
    $80 \%$
  • Correct answer
    D
    $20 \%$

Solution

RMS speed of gas, $\mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$ $\begin{aligned} & \therefore \quad V_{\mathrm{mss}} \alpha \sqrt{\mathrm{T}} \\ & \text { Initial temperature, } \mathrm{T}_{\mathrm{i}}=27+273=300 \mathrm{k} \\ & \text { Final temperature, } \mathrm{T}_{\mathrm{f}}=159+273=432 \mathrm{k} \\ & \% \text { increase in RMS speed }=\frac{\sqrt{432}-\sqrt{300}}{\sqrt{300}} \times 100 \\ & =\frac{20.78-17.32}{17.32} \times 100 \\ & =19.78 \approx 20\end{aligned}$

Hence, the correct answer is option: 'D'.

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