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(A) The expansion occurs in a vacuum,so the work done by the expanding gas is $\Delta W = 0$.The container is perfectly insulated,so the heat exchange

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the initial internal energy of the gas equals its final internal energy

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(A) The expansion occurs in a vacuum,so the work done by the expanding gas is $\Delta W = 0$.The container is perfectly insulated,so the heat exchanged with the surroundings is $\Delta Q = 0$.According to the first law of thermodynamics,$\Delta Q = \Delta U + \Delta W$.Substituting the values,we get $0 = \Delta U + 0$,which implies $\Delta U = 0$.Therefore,$U_i = U_f$,meaning the initial and final internal energies of the gas are equal.Since the gas is not ideal,the expansion results in an increase in the intermolecular potential energy. Because the total internal energy remains constant,this increase in potential energy leads to a decrease in the kinetic energy of the molecules,which consequently causes the temperature of the gas to decrease.

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