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 `u_("m s")` 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)`