Freshly brewed coffee, immediately after being poured into the cup, has an approximate temperature of 85°C (185°F). The coffee becomes safe to drink after it cools to 62°C (143°F). The density of water is 1 kg/liter (1000 kg/ m³), the density of ice is 917 kg/m², the specific heat capacity of water is 4.19 J/g-K, the latent heat for melting is 333 J/g, the entropy of 1 mole of water is 69.91 J/K, the molar mass of water is 18.02g/mol. a) How much ice at 0°C do you need to put into 0.5 liters cup of coffee to cool it down below 60°C? Coffee has almost the same physical parameters as water, for simplicity use water values. If you can’t do part (a), then use any value between 50-100g for the ice mass and continue problem. b) Calculate the change in the entropy of the ice as it melts into water (use Thermodynamic Identity). c) Calculate the total change in the entropy of the ice as it melts into water and then as its temperature rises from 0°C to 60°C. d) Calculate the change in the entropy of the coffee as its temperature drops from 85°C to 60°C. e) Calculate the net change in the entropy of the system during this process. Is the net change positive, negative, or zero? Comment f) What happens to the coffee's Gibbs free energy during this process? Find the change in Gibbs free energy.

Freshly brewed coffee, immediately after being poured into the cup, has an approximate temperature of 85°C (185°F). The coffee becomes safe to drink after it cools to 62°C (143°F). The density of water is 1 kg/liter (1000 kg/ m³), the density of ice is 917 kg/m², the specific heat capacity of water is 4.19 J/g-K, the latent heat for melting is 333 J/g, the entropy of 1 mole of water is 69.91 J/K, the molar mass of water is 18.02g/mol. a) How much ice at 0°C do you need to put into 0.5 liters cup of coffee to cool it down below 60°C? Coffee has almost the same physical parameters as water, for simplicity use water values. If you can’t do part (a), then use any value between 50-100g for the ice mass and continue problem. b) Calculate the change in the entropy of the ice as it melts into water (use Thermodynamic Identity). c) Calculate the total change in the entropy of the ice as it melts into water and then as its temperature rises from 0°C to 60°C. d) Calculate the change in the entropy of the coffee as its temperature drops from 85°C to 60°C. e) Calculate the net change in the entropy of the system during this process. Is the net change positive, negative, or zero? Comment f) What happens to the coffee's Gibbs free energy during this process? Find the change in Gibbs free energy.

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