Question

The root mean square speed of an ideal gas in a closed container of fixed volume is increased from $5\times 10^{2}$ m $s^{- 1}$ to $10^{3}$ m $s^{- 1}$ . Which of the following statement might correctly explain how the change is accomplished?

• A. By heating the gas, the temperature is doubled
• B. By heating the gas, the pressure is quadrupled
• C. By heating the gas, volume is tripled
• D. By heating the gas, the pressure is doubled

Answer 1

Answer: (B)

$u_{r m s}=\sqrt{\frac{3 R T}{M}}=\sqrt{\frac{3 P V}{M}}$

So $\frac{u_{r m s}}{u_{r m s}^{'}}=\frac{5 \times 1 0^{2} m / s}{1 0^{3} m / s}=\frac{1}{2}$

$=\sqrt{\frac{3 P V / M}{3 P ' V / M}}=\sqrt{\frac{P}{P '}}$

$\frac{1}{4}=\frac{P}{P '}$

or $P'=4P.$