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

Let temperature of Jupiter be T .
`{:(" Molar mass of"),(" methane gas"):}} ` = `16.04 xx1010^(-3) kg//mol `
RMS speed of methane gas
`V_(rms)=471.8ms^(-1)`
Gas constant R = 8.31 J/mol/k
`V_(rms)=sqrt((3RT)/m)`
`V_(rms)^2=(3RT)/m`
`:. T =((V_(rms))^2xxm)/(3R)`
`=((471.8)^2xx16.04xx10^(-3))/(3xx8.31)`
`=(3570427xx10^(-3))/(24.93)`
=143 K = -273+143
Temperature of Jupiter is ,
`=-130^@C`.