An ideal gas in a closed container is heated so that the final rms speed of the gas particles increases by 2 times the initial rms speed. If the initial gas temperature is 27° C, then the final temperature of the ideal gas is :

Question

An ideal gas in a closed container is heated so that the final rms speed of the gas particles increases by 2 times the initial rms speed. If the initial gas temperature is 27° C, then the final temperature of the ideal gas is : (A) 1200° C (B) 927° C (C) 827° C (D) 1473° C

Tardigrade Admin · Accepted Answer

As, rms velocity of ideal gas particles is given,

v_{r m s} = \frac{3 k T}{m}

v_{r m s} \propto T

where, temperature

T

is measured in kelvin scale. So, the ratio

\frac{v _{1 r m s}^{2}}{v _{2 r m s}^{2}} = \frac{T _{1}}{T _{2}}

As given,

v_{2 r m s} = 2 v_{1 r m s}

and

T_{1} = 2 7^{\circ} C = 300 K

\Rightarrow \frac{v _{1 r m s}^{2}}{4 v _{1 r m s}^{2}} = \frac{300}{x}

\Rightarrow x = 300 \times 4 = 1200 K

Hence,

1200 K = (1200 - 273)^{\circ} C = 92 7^{\circ} C

Q. An ideal gas in a closed container is heated so that the final rms speed of the gas particles increases by $2$ times the initial rms speed. If the initial gas temperature is $2 7^{\circ} C$ , then the final temperature of the ideal gas is :

$120 0^{\circ} C$

$92 7^{\circ} C$

$82 7^{\circ} C$

$147 3^{\circ} C$

Q. An ideal gas in a closed container is heated so that the final rms speed of the gas particles increases by 2 times the initial rms speed. If the initial gas temperature is 27∘C, then the final temperature of the ideal gas is :

1200∘C

927∘C

827∘C

1473∘C

Q. An ideal gas in a closed container is heated so that the final rms speed of the gas particles increases by $2$ times the initial rms speed. If the initial gas temperature is $2 7^{\circ} C$ , then the final temperature of the ideal gas is :

$120 0^{\circ} C$

$92 7^{\circ} C$

$82 7^{\circ} C$

$147 3^{\circ} C$