The earth has a mass ME = 5.98 · 1024 kg and the moon has a mass MM = 7.36 · 1022 kg. The distance from the center of the earth
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The equation of state for an ideal gas is
where p is the gas pressure, V the volume, n the number of moles, R the gas constant and T the temperature.
The equation of state for the initial condition of the gas is
(1)
While the same equation for the final condition is
(2)
We know that in the final condition, half of the mass of the gas is escaped. This means that the final volume of the gas is half of the initial volume, and also that the final number of moles is half the initial number of moles, so we can write:
If we substitute these relationship inside (1), and we divide (1) by (2), we get
And since the initial temperature of the gas is
, we can find the final temperature of the gas:
where p is the gas pressure, V the volume, n the number of moles, R the gas constant and T the temperature.
The equation of state for the initial condition of the gas is
While the same equation for the final condition is
We know that in the final condition, half of the mass of the gas is escaped. This means that the final volume of the gas is half of the initial volume, and also that the final number of moles is half the initial number of moles, so we can write:
If we substitute these relationship inside (1), and we divide (1) by (2), we get
And since the initial temperature of the gas is