When temperature of an ideal gas is increased from 27^ C to 227^ C , its rms speed is changed from 400 ~m / s to v_s . Then, v_s is

Correct answer: A. 516 ~m / s We know that rms speed is directly proportional to square root of temperature v_ rms T Hence, v_ rms(1) v_ rms(2) = (T_1)/(T_2) aligned & 400 v_ rms(2) = 27+273 227+273 = (300)/(500) & V_ rms(2) = (500)/(300) × 400 & =1.29 × 400=516.39 ~m / s & 516 ~m / s & aligned

JIPMER 2005

Exam: JIPMER
Year: 2005
Subject: Physics
Chapter: Kinetic Theory of Gases

JIPMER 2005 · Physics · Kinetic Theory of Gases

When temperature of an ideal gas is increased from 27^ C to 227^ C...

When temperature of an ideal gas is increased from

27^{\circ} \mathrm{C}

227^{\circ} \mathrm{C}

, its rms speed is changed from

400 \mathrm{~m} / \mathrm{s}

v_s

. Then,

v_s

Options

A $516 \mathrm{~m} / \mathrm{s}$
B $450 \mathrm{~m} / \mathrm{s}$
C $310 \mathrm{~m} / \mathrm{s}$
D $746 \mathrm{~m} / \mathrm{s}$

Correct answer

A. $516 \mathrm{~m} / \mathrm{s}$

Step-by-step solution

We know that rms speed is directly proportional to square root of temperature

\quad \qquad v_{\mathrm{rms}} \propto \sqrt{T}

Hence,

\frac{v_{\mathrm{rms}(1)}}{v_{\mathrm{rms}(2)}}=\sqrt{\frac{T_1}{T_2}}

\begin{aligned} & \frac{400}{v_{\mathrm{rms}(2)}}=\frac{\sqrt{27+273}}{\sqrt{227+273}}=\sqrt{\frac{300}{500}} \\ & V_{\mathrm{rms}(2)}=\sqrt{\frac{500}{300}} \times 400 \\ & =1.29 \times 400=516.39 \mathrm{~m} / \mathrm{s} \\ & \approx 516 \mathrm{~m} / \mathrm{s} \\ & \end{aligned}

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