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............... $^\circ \mathrm{C}$ તાપમાને નાઇટ્રોજન વાયુની $rms$ ઝડપ $127\,^oC$ તાપમાને રહેલ ઑક્સીજન વાયુની $rms$ ઝડપ જેટલી થાય?
$457$
$273$
$350$
$77$
Solution
Rms velocity of gas is
$v_{\mathrm{rms}}=1.73\left(\frac{\mathrm{RT}}{\mathrm{M}}\right)^{\frac{1}{2}};$
$\mathrm{M}=$ molecular mass
For oxygen, $\mathrm{M}=16 \times 2,$
$\mathrm{T}=127^{\circ} \mathrm{C}=127+273=400 \mathrm{K}$
For nitrogen, $\mathrm{M}=17 \times 2, \mathrm{T}=?$
$ \Rightarrow 1.73\left( {\frac{{{\rm{RT}}}}{{\rm{M}}}} \right)_{{O_2}}^{\frac{1}{2}} = 1.73\left( {\frac{{{\rm{RT}}}}{{\rm{M}}}} \right)_{{{\rm{N}}_2}}^{\frac{1}{2}}$
$\Rightarrow\left(\frac{T}{M}\right)_{O_{2}}^{\frac{1}{2}}=\left(\frac{T}{M}\right)_{N_{2}}^{\frac{1}{2}}$
$\Rightarrow \quad \sqrt{T_{N_{2}}}=\sqrt{\frac{M_{N_{2}}}{M_{O_{2}}} T_{O_{2}}}=\sqrt{\frac{28}{32} \times 400}$
$\quad=\sqrt{\frac{7}{8} \times 400}$
$\Rightarrow T_{N_{2}}=\frac{7}{8} \times 400=350 \mathrm{K}$
$T_{N_{2}}=350 \mathrm{K}-273 \mathrm{K}=77^{\circ} \mathrm{C}$
