Question

If temperature changes from 27°C to 127°C, the
relative percentage change in rms velocity is

(a) 1.56
(b) 2.56
(c) 15.6
(d) 82.4​

Answer 1

Answer is Option (c)

Explanation:

$V_r_m_s = \sqrt (\frac {3RT}{MW})$

⇒ $V_r_m_s = \sqrt (\frac {3R (27 + 273)}{MW})$

⇒ $V_r_m_s = \sqrt (\frac {3 \times (300)R}{MW})$

⇒ $V_r_m_s = 30 \sqrt (\frac {R}{MW})$

Now,  

$V'_r_m_s = \sqrt (\frac {3RT}{MW})$

$V'_r_m_s = \sqrt (\frac {3(400)R}{MW})$

$V'_r_m_s = 20\times \sqrt 3 (\sqrt (\frac {R}{MW}))$

Now, Change in V = $\frac {V'_r_m_s - V_r_m_s}{V_r_m_s} \times 100$

= $\frac {20\sqrt 3(\sqrt (\frac {R}{MW}) - 30(\sqrt (\frac {R}{MW})}{30(\sqrt (\frac {R}{MW})} \times 100$

= $\frac {34.6 - 30}{30} \times 100$

= $\frac {46}{3}$

= 15.6 (Option (c))