Question

Match the Column-I with Column-II for ideal gases.

Answer 1

(A) If temperature of given gas is increased, all three speeds, ie, average speed (v), root mean square speed (u) and most probable speed ($\alpha$) of gas molecules will increase.
$\alpha =\sqrt{\frac{2RT}{M}}$
$u=\sqrt{\frac{3RT}{M}}$
$v=\sqrt{\frac{8RT}{\pi M}}$
(B) If the pressure of a given gas is increased at constant temperature, all three speeds, ie, average speed (v), root mean square speed (u) and most probable speed ($\alpha$) of gas molecules will increase.
$\alpha =\sqrt{\frac{2PV}{M}}$
$u=\sqrt{\frac{3PV}{M}}$
$v=\sqrt{\frac{8PV}{\pi M}}$
(C) If the density of a given gas is lowered at constant temperature, all three speeds, ie, average speed (v), root mean square speed (u) and most probable speed ($\alpha$) of gas molecules will decrease.
$\alpha =\sqrt{\frac{2P}{d}}$
$u=\sqrt{\frac{3P}{d}}$
$v=\sqrt{\frac{8P}{\pi d}}$
(D) If the volume of a given gas is increased at constant temperature, all three speeds, ie, average speed (v), root mean square speed (u) and most probable speed ($\alpha$) of gas molecules will increase.
$\alpha =\sqrt{\frac{2PV}{M}}$
$u=\sqrt{\frac{3PV}{M}}$
$v=\sqrt{\frac{8PV}{\pi M}}$