Question

The temperature of a gas is raised from ${27}^{0}C$ to ${927}^{0}C$. The root mean square speed :

• A. $\sqrt{\frac{927}{27}}$ times the earlier value
• B. Remains same
• C. Gets halved
• D. Gets doubled

Answer 1

Answer: (D)

Gets doubled

The root mean square speed is,

$V_{rms}=\sqrt{\frac{3RT}{m}}$. . . . .(1)

From the above equation,

$V_{rms}\propto \sqrt{T}$

$\frac{V_{1rms}}{V_{2rms}}=\sqrt{\frac{T_1}{T_2}}=\sqrt{\frac{27+273}{927+273}}$

$V_{2rms}=V_{1rms}\sqrt{\frac{1200}{300}}$

$V_{2rms}=2V_{1rms}$

The correct option is D.