Question

For a gas sample with N number of molecules, function N(v) is given by N(V)=V²for 0 < V < V₀ and N (V) = 0 for V > V_o. Where dN is number of molecules in speed range V to V + dV. The rms speed of molecules is :

• A. $\sqrt { \frac { 2 } { 5 } }$V_o
• B. $\sqrt { \frac { 3 } { 5 } }$V_o
• C. $\sqrt { 2 }$V_o
• D. $\sqrt { 3 }$V_o

Answer 1

Answer: (B)

$\sqrt { \frac { 3 } { 5 } }$V_o

Answer 2

V_rms² = $\frac { 1 } { N } \int _ { 0 } ^ { \infty } N ( V ) V ^ { 2 } d V$

=

v_rms = $\sqrt { \frac { 3 } { 5 } }$.v₀.