MCQ
The temperature at which the root mean square velocity of a molecule will be doubled than at $100°C$
- ✓$1219°C$
- B$1492°C$
- C$400°C$
- D$400\, K$
✓
Answer
Correct option: A.
$1219°C$
a
$R.M.S.$ velocity $\sqrt{\frac{3 R T}{M}}$
$R.M.S.$ velocity $\sqrt{\frac{3 R T}{M}}$
How, when other terms are constant, $(R \cdot M . S) \propto \sqrt{T}$.
$\frac{(R \cdot M \cdot S)_{1}}{(R \cdot M \cdot S)_{2}}=\frac{\sqrt{T_{1}}}{\sqrt{T_{2}}}$
Here, $(R \cdot M \cdot S)_{2}=2 \cdot(R \cdot M \cdot S)_{1}$
$T_{1} =100^{\circ} C =(100+273) K =373 \; K$
$\therefore \frac{(R \cdot M \cdot S)_{1}}{2 \cdot(R \cdot M \cdot S)} =\frac{\sqrt{373}}{\sqrt{T_{2}}}$
$\sqrt{T_{2}} =2 \cdot \sqrt{373}$
$T_{2} =1492 \; K$ [squaring both sides]
Convert into celcius.,
$T_{2}=(1492-273)^{\circ} C =1219^{\circ} C$
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