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Question
If the rms speed of methane gas in the Jupiter’s atmosphere is 471.8 ms−1, shows that the surface temperature of Jupiter is sub-zero.
Solution
RMS speed of methane gas (vrms) = 471.8 ms−1
Molar mass of methane gas (M) = 16.04 g per mol
M = 16.04 × 10−3 kg/mol
Gas constant R = 8.31 J mol−1 K−1
vrms = `sqrt((3"RT")/"M")`
(vrms)2 = `(3"RT")/"M"`
T = `(("v"_"rms")^2 xx "M")/(3"R")`
= `((471.8)^2 xx 16.04 xx 10^-3)/(3 xx 8.31)`
= `(3.57 xx 10^6 xx 10^-3)/24.93`
= 0.143 × 103
T = 143 K − 273
T = − 130°C
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