Question

A student wants to investigate the thermodynamic properties of a system undergoing a non-equilibrium process. The system is initially at a temperature of 300 K and pressure of 1 atm. A sudden expansion of the system causes the pressure to drop to 0.5 atm while maintaining a constant temperature. Calculate the change in entropy of the system during the process assuming ideal gas behavior.

Answer 1

To calculate the change in entropy  S  for an ideal gas undergoing an isothermal expansion, we can use the following equation:S = n * R * ln V2/V1 where n is the number of moles of the gas, R is the ideal gas constant  8.314 J/molK , V1 is the initial volume, and V2 is the final volume. Since we are not given the number of moles or the volume, we can use the ideal gas law to relate pressure, volume, and temperature:PV = nRTSince the temperature remains constant, we can write the ratio of the initial and final volumes in terms of the initial and final pressures:V2/V1 = P1/P2Given the initial pressure  P1  of 1 atm and the final pressure  P2  of 0.5 atm, we can calculate the ratio of the volumes:V2/V1 = 1/0.5 = 2Now we can plug this value into the entropy equation:S = n * R * ln 2 Since we don't know the number of moles  n , we can leave the answer in terms of n:S = n * 8.314 J/molK * ln 2 S  n * 5.76 J/molKThe change in entropy of the system during the process is approximately 5.76 J/molK times the number of moles of the gas.