Question

Prove that P = 1/3pv².

Answer 1

We know that, root mean square velocity

v = \(\sqrt\frac{3RT}M\)

\(\because\)Pv = nRT

n = 1

v = \(\sqrt\frac{3pv}M\) 

v = \(\sqrt\frac{3pv}{M/v}\)

v = \(\sqrt\frac{3p}p\) 

v² = \(\frac{3p}p\)

p = \(\frac13pv^2\)