As the closest planet to the Sun Mercury\'s day-side surface is a blistering 725

Question

As the closest planet to the Sun Mercury's day-side surface is a blistering 725K (845 degree F). I'm curious what happens when I dump molecular hydrogen (H2) on the surface, Calculate the molar mass of molecular hydrogen. Calculate the rms speed of the molecules if I dumped them on the day side of Mercury. Escape velocity from Mercury's surface is 4.3km/s. If the rms speed of the gas is within two or three times the escape velocity, the planet's gravity definitely won't be able to hold it. Will the hydrogen I dumped on the surface stay there or escape into space? For each scenario, decide if the temperature increases, decreases, or stays the same, a. 50J of heat are added and -25 J of work done on the gas. 50J of heat are removed and -25J work done on the gas. 10J of heat are added and -10J of work is done on the gas.

Explanation / Answer

1.a)Molar mass of hydrogen =1.007 g/mole

for hydroggen molecule=2x1.007=2.014g/mole

b)v(rms) = sqrt(3RT/M)

v(rms) = sqrt(3 x 8.3145 J/K mol s x 725 / 0.002014 kg)
v(rms) = 1730 m/s

c)since 3 times rms =5160m/s , hydrogen will stay on the surface.

2.a)decrease

b)increase

c)same

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