Question

The atmosphere of Jupiter is essentially made up of hydrogen, H2. For H2, the specific gas constant is 4157 J/(kg K). The acceleration of gravity of Jupiter is 24.9 m/s2 . Assuming an isothermal atmosphere with a temperature of 150 K and assuming that Jupiter has a definable surface, calculate the altitude above that surface where the pressure is one-half the surface pressure

Answer 1

Answer:

h=17357.9m

Explanation:

The atmospheric pressure is just related to the weight of an arbitrary column of gas in the atmosphere above a given area. So, if you are higher in the atmosphere less gass will be over you, which means you are bearing less gas and the pressure is less.

To calculate this, you need to use the barometric formula:

$P=P_0e^{-\frac{Mg}{RT}h}$

Where R is the gas constant, M the molar mass of the gas, g the acceleration of gravity, T the temperature and h the height.

Furthermore, the specific gas constant is defined by:

$R_{H_2}=\frac{R}{M}$

Therefore yo can write the barometric formula as:

$P=P_0e^{-\frac{g}{R_{H_2}T}h}$

at the surface of the planet (h =0) the pressure is $P_0[\tex]. The pressure at the height requested is half of that:

[tex]P=\frac{P_0}{2}$

applying to the previuos equation:

$\frac{P_0}{2} =P_0e^{-\frac{g}{R_{H_2}T}h}$

solving for h:

h=17357.9m