Molecular velocities of two gases at the same temperature (T) are u1 and u2. Their masses are m1 and m2 respectively. Which of the following expressions is correct at temperature T?

Question

Molecular velocities of two gases at the same temperature (T) are u1 and u2. Their masses are m1 and m2 respectively. Which of the following expressions is correct at temperature T? (A) (m1/u12)=(m2/u22) (B) m1 u1=m2 u2 (C) (m1/u1)=(m2/u2) (D) m1 u1 2=m2 u2 2

Tardigrade Admin · Accepted Answer

We know u × √(T/m) but as T is same for both gases Hence u propto (1/√m) ∴ (u1/u2)=√(m2/m1) or (u1 2/u2 2)=(m2/m1) or m1 u1 2=m2 u2 2

Q. Molecular velocities of two gases at the same temperature $(T)$ are $u_{1}$ and $u_{2}$ . Their masses are $m_{1}$ and $m_{2}$ respectively. Which of the following expressions is correct at temperature T?

$\frac{m _{1}}{u _{1}^{2}} = \frac{m _{2}}{u _{2}^{2}}$

$m_{1} u_{1} = m_{2} u_{2}$

$\frac{m _{1}}{u _{1}} = \frac{m _{2}}{u _{2}}$

$m_{1} u_{1}^{2} = m_{2} u_{2}^{2}$

We know $u \times \frac{T}{m}$
but as $T$ is same for both gases
Hence $u \propto \frac{1}{m}$
$∴ \frac{u _{1}}{u _{2}} = \frac{m _{2}}{m _{1}}$
or $\frac{u _{1} ^{2}}{u _{2} ^{2}} = \frac{m _{2}}{m _{1}}$
or $m_{1} u_{1}^{2} = m_{2} u_{2}^{2}$

Q. Molecular velocities of two gases at the same temperature (T) are u1​ and u2​. Their masses are m1​ and m2​ respectively. Which of the following expressions is correct at temperature T?

u12​m1​​=u22​m2​​

m1​u1​=m2​u2​

u1​m1​​=u2​m2​​

m1​u1​2=m2​u2​2