Question

For Gaseous state, if most probable speed is denoted by $C^{+}$, average speed by $\overline{C}$ and mean square speed by $C$$, then for a large number of molecules the ratios of these speeds are:

• A. $C^{+}:\overline{C}:C=1.225:1.128:1$
• B. $C^{+}:\overline{C}:C=1.128:1.225:1$
• C. $C^{+}:\overline{C}:C=1:1.128:1.225$
• D. $C^{+}:\overline{C}:C=1:1.225:1.128$

Answer 1

Answer: (C)

$C^{+}:\overline{C}:C=1:1.128:1.225$

We know that

$C^{+}=\sqrt{\frac{2RT}{M}},\overline{C}=\sqrt{\frac{8RT}{\pi M}},C=\sqrt{\frac{3RT}{M}}$

We have to calculate:-

$C^{+}:\overline{C}:C=\sqrt{\frac{2RT}{M}},\sqrt{\frac{8RT}{\pi M}},\sqrt{\frac{3RT}{M}}$

$=1:1.128:1.225$

As we know

$P=\frac{DRT}{MW}$

$dt=const$

$d_1{T}_1=d_2{T}_2$

$D\times 300=0.75d\times T_2$

$T_2=100\times 4$

$T_2=400K$