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.

If the rms speed of methane gas in the Jupiter's atmosphere is 471.8ms

1.	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.
Answer» Solution :RMS speed of methane gas `(nu_(rms))=471.8ms^(-1)` MOLAR mass of methane gas (M) 16.04 g PER mol `M=16.04xx10^(-3)kg/mol` Gsa constant `R=8.31 J mol^(-1)K^(-1)` `nu_(rms)=sqrt((3RT)/M)` `(nu_(rms))^(2)=(3RT)/M` `T=((nu_(rms))^(2)xxM)/(3R)=((471.8)^(2)xx16.04xx10^(-3))/(3xx8.31)` `(3.57xx10^(-6)xx10^(-3))/(24.93)=0.143xx10^(3)` T=143K-273 `T=-130^(@)C`