If the rms speed of methane gas in the Jupiter's atmosphere is `471.8ms^(-1)`, show that the surface temperature of Jupiter is sub-zero.

Explanation

RMS speed of methane gas
`=471.8ms^(-1)=V_(rms)`
Sub-zero temperature
Molar mass of methane gas
`=16.04xx10^(-3)kgmol^(-1)`
Surface temperature of Jupiter T = ?
Gas constant R = 8.31
`V_(rms)=sqrt((3RT)/(m))impliesT=(V_(rms)^(2)m)/(3R)`
`=((471.8)^(2)xx16.04xx10^(-3))/(3xx8.31)=(3.549456xx10^(-3))/(24.9)`
`T=143k" (or)"-273+143`
`T=-130^(@)C`