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BITSAT 2013
Exam
BITSAT
Year
2013
Subject
Physics
Chapter
Kinetic Theory of Gases

BITSAT 2013 · Physics · Kinetic Theory of Gases

The temperature of an ideal gas is increased from 27^ ^ C to 127^ ^...

The temperature of an ideal gas is increased from 27∘C27^{{}^{\circ}} \mathrm{C} to 127∘C127^{{}^{\circ}} \mathrm{C}, then percentage increase in vrms\mathrm{v}_{\mathrm{rms}} is

Options

  1. A37%37 \%
  2. B11%11 \%
  3. C33%33 \%
  4. D15.5%15.5 \%

Correct answer

D. 15.5%15.5 \%

Step-by-step solution

We know, Vmms=3RTM⇒%\mathrm{V}_{\mathrm{mms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}\Rightarrow \% increase in Vrms=3RT2M−3RT1M3RT1M×100=T2−T1T1×100=400−300300×100=20−17.3217.32×100=15.5%\begin{array}{l}\mathrm{V}_{\mathrm{rms}}=\frac{\sqrt{\frac{3 \mathrm{R} \mathrm{T}_{2}}{\mathrm{M}}}-\sqrt{\frac{3 \mathrm{RT}_{1}}{\mathrm{M}}}}{\sqrt{\frac{3 \mathrm{RT}_{1}}{\mathrm{M}}}} \times100 \\ =\frac{\sqrt{\mathrm{T}_{2}}-\sqrt{\mathrm{T}_{1}}}{\sqrt{\mathrm{T}_{1}}} \times100 \\ =\frac{\sqrt{400}-\sqrt{300}}{\sqrt{300}} \times100 \\ =\frac{20-17.32}{17.32} \times100=15.5 \% \end{array}
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