114 3 THE SECOND LAW 3.15(b) A certain heat engine operates between 1000 K and 500 K. (a) What is the maximum efficiency of the engine? (b) Calculate the maximum work that can be done by for each 1.0 kJ of heat supplied by the hot source. (c) How much heat is discharged into the cold sink in a reversible process for each 1.0 kJ supplied by the hot source? 3.16(a) Suppose that 3.0 mmol N,(g) occupies 36 cm' at 300 K and expands to 60 cm. Calculate AG for the process. 3.16(b) Suppose that 2.5 mmol Ar(g) occupies 72 dm' at 298 K and expands to 100 dm. Calculate AG for the process. 3.17(a) The change in the Gibbs energy of a certain constant-pressure process was found to fit the expression AG/1=-85.40+ 36.5(T/K). Calculate the value of AS for the process. 3.17(b) The change in the Gibbs energy of a certain constant-pressure process was found to fit the expression AG/J-73.1+42.8(77K). Calculate the value of AS for the process. 3.18(a) Calculate the change in Gibbs energy of 35 g of ethanol (mass density 0.789 g cm³) when the pressure is increased isothermally from 1 atm to 3000 atm. 3.18(b) Calculate the change in Gibbs energy of 25 g of methanol (mass density 0.791 g cm³) when the pressure is increased isothermally from 100 kPa to 100 MPa. F 3 F 3 C t C L 3 t 3 F Problems* Assume that all gases are perfect and that data refer to 298 K unless otherwise stated. Numerical problems 3.1 Calculate the difference in molar entropy (a) between liquid water and ice at -5°C, (b) between liquid water and its vapour at 95°C and 1.00 atm. The differences in heat capacities on melting and on vaporization are 37.3 JK moland-41.9JK mol', respectively. Distinguish between the entropy changes of the sample, the surroundings, and the total system, and discuss the spontaneity of the transitions at the two temperatures. 3.2 The heat capacity of chloroform (trichloromethane, CHCI,) in the range 240 K to 330 K is given by CJK mol)=91.47+7.5x10 (77K). In a particular experiment, 1.00 mol CHCI, is heated from 273 K to 300 K. Calculate the change in molar entropy of the sample. 3.3 A block of copper of mass 2.00 kg (C-24.441 K' mol¹) and temperature 0°C is introduced into an insulated container in which there is 1.00 mol H,O(g) at 100°C and 1.00 atm. (a) Assuming all the steam is condensed to water, what will be the final temperature of the system, the heat transferred from water to copper, and the entropy change of the water, 144/1097 9:57 PM 69% I E S v F Γ C 3 a D