Question

The temperature of an ideal gas is reduced from $927^{o}C$to $27^{o}C$. The rms velocity of the molecules becomes

• A. Double the initial value
• B. Half of the initial value
• C. Four times the initial value
• D. Ten times the initial value

Answer 1

Answer: (B)

Half of the initial value

Answer 2

$u = \sqrt{\frac{3RT}{M}}$

∴ $\frac{u_{1}}{u_{2}} = \sqrt{\frac{T_{1}}{T_{2}}} = \sqrt{\frac{927 + 273}{27 + 273}} = \sqrt{\frac{1200}{300}} = \sqrt{4} = 2$

∴$u_{2} = \frac{1}{2}u_{1}$