When temperature of an ideal gas is increased from 27° C to 227° C, its rms speed is changed from 400 m / s to vs. The vs is :

Question

When temperature of an ideal gas is increased from 27° C to 227° C, its rms speed is changed from 400 m / s to vs. The vs is : (A) 516 m/s (B) 450 m/s (C) 310 m/s (D) 746 m/s

Tardigrade Admin · Accepted Answer

We know that rms speed is directly proportional to square root of temperature.

v_{r m s} \propto T

Hence,

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

\frac{400}{v _{r m s (2)}} = \frac{27 + 273}{227 + 273}

= \frac{300}{500}

v_{r m s (2)} = v = \frac{500}{300} \times 400

= 1, 29 \times 400 = 516.39 m / s

\approx 516 m / s

Q. When temperature of an ideal gas is increased from 27∘C to 227∘C, its rms speed is changed from 400m/s to vs​. The vs​ is :

516 m/s

450 m/s

310 m/s

746 m/s

We know that rms speed is directly proportional to square root of temperature. vrms​∝T​ Hence, vrms(2)​vrms​(1)​=T2​T1​​​ vrms(2)​400​=227+273​27+273​​ =500300​​ vrms(2)​=v=300500​​×400 =1,29×400=516.39m/s ≈516m/s

Q. When temperature of an ideal gas is increased from $2 7^{\circ} C$ to $22 7^{\circ} C$ , its rms speed is changed from $400 m / s$ to $v_{s}$ . The $v_{s}$ is :