Question

The temperature of an ideal gas is increased from 27°C to 127 °C, then percentage increase in vrms is

• A. 37%
• B. 11%
• C. 33%
• D. 15.5%

Answer 1

Answer: (D)

15.5%

Answer 2

$V_{rms} = \sqrt{\frac{3RT}{M}}$

% increase in $V_{rms} = \frac{\sqrt{\frac{3/RT_{2}}{M}} - \sqrt{\frac{3RT_{1}}{M}}}{\sqrt{\frac{3RT_{1}}{M}}} \times 100$

$= \frac{\sqrt{T_{2}} - \sqrt{T_{1}}}{\sqrt{T_{1}}} \times 100 = \frac{\sqrt{400} - \sqrt{300}}{\sqrt{300}} \times 100$

$= \frac{20 - 17.32}{17.32} \times 100 = 15.5\%$