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) = T_(A)gt T_(C) gt T_(B)`
C. `T_(D) gt T_(A)= T_(B) gt T_(C)`
D. `T_(B) gt T_(C)gt T_(A) gt T_(D)`

Answer

C

Explanation

`v_("rms") = sqrt((3KT)/(m)) implies T = (mv_("rms")^(2))/(3K) because T prop mv_("rms")^(2)`