Question

A sealed container with negligible coefficient of volumetric expansion contains helium (a monoatomic gas). When it is heated from 300 K to 600 K, the average KE of helium atoms is

• A. halved
• B. unchanged
• C. doubled
• D. increased by factor $\sqrt 2$

Answer 1

Answer: (C)

doubled

Answer 2

$K =\frac{1}{2} mv _{ ms }^{2}$
$v _{ rms }=\sqrt{\frac{3 KT }{ M }}$
$v _{ rms } \propto \sqrt{ T }$
$\frac{ K _{2}}{ K _{1}}=\left(\sqrt{\frac{ T _{2}}{ T _{1}}}\right)^{2}$
$K _{2}= K _{1} \frac{ T _{2}}{ T _{1}}$
$K _{2}= K _{1} \frac{600}{300}$
$\Rightarrow K _{2}=2 K _{1}$