Final answer:
The change in entropy for an ideal diatomic gas expanding isothermally into an evacuated tank is calculated using the formula ΔS = nRln(Vf/Vi), which yields a positive value indicating spontaneous and irreversible expansion.
Step-by-step explanation:
The question at hand relates to the concept of entropy change during an isothermal expansion of an ideal diatomic gas into a vacuum. Since work is defined as the product of pressure and volume change and the pressure in a vacuum is zero, no pressure-volume work is done when the gas expands into the evacuated tank. However, even without external work, there is a change in the entropy of the gas because the number of microstates of the system increases when the gas expands from tank A to tank B.
The entropy change (ΔS) for an isothermal expansion can be calculated using the formula:
ΔS = nRln(Vf/Vi)
Where n is the number of moles of the gas, R is the ideal gas constant, and Vf and Vi are the final and initial volumes, respectively. Since tank B is initially evacuated, and tanks A and B are identical, the final volume of the gas would be twice the initial volume. Therefore, the entropy change would be positive and the expression simplifies to:
ΔS = 20mol * R * ln(2)
In conclusion, the entropy of the gas increases as it expands from tank A to tank B, indicating that the process is spontaneous and irreversible.