Question

Calculate the entropy change (∆S) when a container of volume 1.0 L is filled with 1.0 mol of ideal gas at a temperature of 300 K and a pressure of 1.0 atm, and then the gas is allowed to expand irreversibly to fill a volume of 2.0 L against a constant external pressure of 0.5 atm at the same temperature.

Answer 1

To calculate the entropy change  S  for this process, we can use the formula for the entropy change of an ideal gas during an isothermal expansion: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.In this case, we have:n = 1.0 molR = 8.314 J/molKV1 = 1.0 LV2 = 2.0 LNow we can plug these values into the formula:S =  1.0 mol  *  8.314 J/molK  * ln 2.0 L / 1.0 L S =  1.0 mol  *  8.314 J/molK  * ln 2 S  5.76 J/KSo the entropy change for this process is approximately 5.76 J/K.