Question

Gas molecules each of mass ${10}^{-26}kg$ are taken in a container of volume $1d{m}^3$. The root mean square speed of gas molecules is $1km{sec}^{-1}$. What is the temperature of gas molecules.
(Given : $N_A=6\times {10}^{23};R=8J/mol.K$)

• A. 298 K
• B. 25 K
• C. 250 K
• D. 2500 K

Answer 1

Answer: (C)

250 K

Man of each gas molecule $={10}^{-26}kg$.

volume of cowaiver $=1d{m}^3$

Root mean square speed $Urm=\sqrt{\frac{3RT}{M}}$

$1|cm|5=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3kT}{m}}$

$1000=\sqrt{\frac{3\times 8\times T}{6\times {10}^{23}\times {10}^{26}}}$

$1000\times 1000=\frac{4.T}{{10}^{-3}}$

$4.T=1000$

$T=250K$