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Ideal gas problem involving heat, entropy, and work

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Note that in this problem the total volume stays constant and that the pressure in both sides is always equal. Let's calculate the number of helium atoms, the number of N_{2} atoms and the initial volume of the helium.

The atomic mass of helium is 4.002602u. This means that 0.1 kg corresponds to
1.50456*10^(25) helium atoms.

The initial volume then follows from the ideal gas law:

P_{initial}V_{He, initial} = N_{He} kT_{initial}

Inserting P_{initial} = 95*10^(3)Pa, T_{initial}= 293.15 K gives:

V_{He, initial} = 0.641 m^3

The initial volume of the N_{2} is 0.2 m^3, so we always have that:

V_{He} + V_{N_{2}} = 0.841 m^3

Using the ideal gas law we can also calculate the number of N_{2} molecules:

N_{N_{2}} = 4.6944*10^(24)

In the problem it is given that ...

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