Question

For an ideal gas, how will be the temperature changed if the average speed of the molecules of the gas is doubled?

• A. Remains the same
• B. Is doubled
• C. Is halved
• D. Is quadrupled
• E. Is quartered

Answer 1

Answer: (D)

Is quadrupled

Velocity of the ideal gas molecule $v=\sqrt{\frac{3RT}{M}}$

$\therefore$ $v^2\propto T$

$⟹$ $\frac{(v^{\prime }{)}^2}{v^2}=\frac{T^{\prime }}{T}$

Given : $v^{\prime }=2v$

$\therefore$ $\frac{(2v{)}^2}{v^2}=\frac{T^{\prime }}{T}$

$⟹T^{\prime }=4T$