Four containers are filled with monoatomic ideal gases. For each container , the number of moles , the mass of an individual atom and the rms speed of the atoms are expressed in terms of n , m and `v_("rms")` respectively . If `T_(A) , T_(B) , T_(C)` and `T_(D)` are their temperatures respectively then which one of the options correctly represents the order ?

Options

A. `T_B = T_C gt T_A gt T_D`
B. `T_D gt T_A gt T_C gt T_B`
C. `T_D gt T_B = T_B gt T_C`
D. `T_B gt T_C gt T_A gt T_D`

Answer

C

Explanation

`V_("m s") = sqrt((3kT)/(m)) rArr T = (m V_("m s")^2)/(3k )`Where k is the Boltzmann constant
`T_A = (4 m V_("m s")^2)/(3k), T_B=(4mV_("m s")^2)/(3k), T_C = (3m V_("m s")^2)/(3k) , T_B = (8m V_("m s")^2)/(2k)`
Hence `T_D gt T_A =T_B gt T_C`