MCQ
The $r.m.s.$ speed of a certain gas is v at $400\,K.$ The temperature at which the $r.m.s.$ speed becomes two times, will be ...... $K$
- A$800$
- ✓$1600 $
- C$1200$
- DNone of these
✓
Answer
Correct option: B.
$1600 $
b
${v_{rms}} \propto \sqrt T $
${v_{rms}} \propto \sqrt T $
$\Rightarrow$ $\frac{{{T_2}}}{{{T_1}}} = \frac{{v_2^2}}{{v_1^2}} = \frac{{4{v^2}}}{{{v^2}}} = 4$
$\Rightarrow$ ${T_2} = 4{T_1} = 4 \times 400 = 1600\,K$
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