3.19
a. 1.000 mol of helium is compressed reversibly and isothermally from a volume of 100.00 L and a temperature of 298.15 K to a volume of 50.00 L . Calculate \( \Delta \mathrm{S}, \mathrm{q} \), w, and \( \Delta \mathrm{U} \) for the process. Calculate \( \Delta \mathrm{S}_{\text {sur }} \) and \( \Delta \mathrm{S}_{\text {univ. }} \).
b. Calculate the final temperature, \( \Delta \mathrm{S}, \mathrm{q}, \mathrm{w}, \Delta \mathrm{U}, \Delta \mathrm{S}_{\text {surr }} \), and \( \Delta \mathrm{S}_{\text {univ }} \) if the gas is compressed adiabatically and reversibly from the same initial state to a final volume of 50.00 L .
c. The gas is compressed adiabatically and irreversibly from the same initial state to the same final volume with \( \mathrm{P}_{\text {ext }}=1.000 \mathrm{~atm} \). What can you say about the final temperature, \( \Delta \mathrm{S}, \mathrm{q}, \mathrm{w}, \Delta \mathrm{U}, \Delta \mathrm{S}_{\text {surr }} \), and \( \Delta \mathrm{S}_{\text {univ? }} \) ?
d. The gas is compressed isothermally and irreversibly from the same initial state to the same final volume with \( P_{\text {ext }}=1.000 \mathrm{~atm} \). What can you say about \( \Delta \mathrm{S}, \mathrm{q}, \mathrm{w}, \Delta \mathrm{U}, \Delta \mathrm{S}_{\text {surr }} \), and \( \Delta \mathrm{S}_{\text {univ }} \) ?
