The root mean square speed of an ideal gas in a closed container of fixed volume is increased from 5× 102 m s- 1 to 103 m s- 1 . Which of the following statement might correctly explain how the change is accomplished?

Question

The root mean square speed of an ideal gas in a closed container of fixed volume is increased from 5× 102 m s- 1 to 103 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

Tardigrade Admin · Accepted Answer

ur m s=√(3 R T/M)=√(3 P V/M) So (ur m s/ur m s')=(5 × 1 02 m / s/1 03 m / s)=(1/2) =√(3 P V / M/3 P ' V / M)=√(P/P ') (1/4)=(P/P ') or P'=4P.

Q. The root mean square speed of an ideal gas in a closed container of fixed volume is increased from $5 \times 1 0^{2}$ m $s^{- 1}$ to $1 0^{3}$ m $s^{- 1}$ . Which of the following statement might correctly explain how the change is accomplished?

By heating the gas, the temperature is doubled

By heating the gas, the pressure is quadrupled

By heating the gas, volume is tripled

By heating the gas, the pressure is doubled

$u_{r m s} = \frac{3 RT}{M} = \frac{3 P V}{M}$

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

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

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

or $P^{'} = 4 P .$

Q. The root mean square speed of an ideal gas in a closed container of fixed volume is increased from 5×102 m s−1 to 103 m s−1 . Which of the following statement might correctly explain how the change is accomplished?