When pressure remaining constant, at what temperature will the $r.m.s.$ speed of a gas molecules increase by $10 \%$ of the r.m.s. speed at $STP$?
A$57.3 K$
B$57.3^{\circ} C$
C$557.3 K$
D$-57.3^{\circ} C$
Medium
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B$57.3^{\circ} C$
b (b)
$V=\sqrt{\frac{3 R T}{M}} \text { or } V=K \sqrt{T}$
$\text { Let } \frac{V \times 110}{100}=K \sqrt{T_2}$
$\frac{V}{1.1} V=\sqrt{\frac{T}{T_2}}$
$T_2=1.21 T$
$\text { Putting } T=273 \,K$
$T_2=57.33^{\circ} C$
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