A gas is filled in a rigid container at pressure $P_{0}$ . If the mass of each molecule is halved keeping the total number of molecules same and their r.m.s speed is doubled then find the new pressure.

Open in App

Solution

right container = neither compressible nor expansible
As volume is constant
Maxwell's equation of his kinetic theory $\Rightarrow$
$P V = \frac{1}{3} n u_{x m s}^{2} m$

$P V = \frac{1}{3} M V_{r m s}^{2}$

$U_{r m s} = \sqrt{\frac{3 P V}{M}}$
As $P_{1} = P_{0}, V_{1} = V_{2} = V$

$m_{1} = m, m_{2} = m / 2$

$n_{1} = n_{2} = n$

$u_{r m s_{1}} = \frac{U_{r m s_{2}}}{2}$
Now,
$2 U_{r m s_{1}} = U_{r m s_{2}}$

$\Rightarrow 2 \sqrt{\frac{3 p_{1} v_{1}}{n_{1} m_{1}}} = \sqrt{\frac{3 p_{2} v_{2}}{n_{2} m_{2}}}$

$\Rightarrow 2 \sqrt{\frac{3 P_{0} V}{n m}} = \sqrt{\frac{3 P_{2} V}{n m / 2}}$

$\Rightarrow 4 P_{0} = 2 P_{2}$

$\Rightarrow P_{2} = 2 P_{0}$ (Ans)

Suggest Corrections

Similar questions

P_{c}

A gas is filed in a rigid container at pressure $P^{0}$ . If the mass of each molecule is halved

Keeping the total number of molecules same and their r.m.s

speed is doubled then find the new pressure.

P_{0}

400 m/s

27^{\circ} C

10^{5} {N/m}^{2}

P_{0}

P

Join BYJU'S Learning Program