Question

If the absolute temperature of a gas in a fixed volume is quadrupled, then the velocity in initial and final states would be related as

• A. $v_f=4v_i$
• B. $v_f=v_i/4$
• C. $v_f=v_i/2$
• D. $v_f=2v_i$

Answer 1

Answer: (D)

$v_f=2v_i$

If the absolute temperature of a gas in a fixed volume is quadrupled, then the velocity in initial and final states would be related as $v_f=2v_i$
Velocity is directly proportional to the square root of temperature.
$v\propto \sqrt{T}$
$\frac{v_f}{v_i}=\sqrt{\frac{T_f}{T_i}}$
$\frac{v_f}{v_i}=\sqrt{\frac{4T_i}{T_i}}$
$\frac{v_f}{v_i}=\sqrt{4}$
$\frac{v_f}{v_i}=2$
$v_f=2v_i$.
Thus, the option (D) is the correct answer.