In the future, interstellar travel becomes possible. People start to reach out to other planets to

harvest resources from them. Neptune's atmosphere is a gaseous mixture which consists of

80% (mole fraction) hydrogen (H₂), 18.5% helium (He) and 1.5% methane (CH4).

Both hydrogen and methane are of great importance in multiple aspects of modern technologies

such as fertiliser production and electricity generation.

To bring these useful resources back to the planet Earth, 133kg of the gaseous mixture is

compressed to 2.5 MPa and 132K in a container. The mixture is then separated adiabatically

while maintaining the same pressure and temperature. That is, the pressure and temperature of

each of the separated gases is equal to the mixture pressure and temperature within the

container.

Determine the minimum power required for the separation process in MJ.

Assume ideal gas behavior and that the surroundings temperature is the same as that of the

mixture.

(You may use the molar mass: MH₂ = 2kg/kmol, MHe = 4kg/kmol and

MCH 16kg/kmol and the molar gas constant R = 8.3145kJ/kmolK)

Give your answer to 2 decimal places.

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