Entropy and 2nd Law of Thermodynamics

Is it possible… …for a glass of water in a warm room to spontaneously freeze (releasing it’s thermal energy into the air and causing the internal energy of the water to decrease and the air to increase) …for the air in a room to spontaneously “decide” to only occupy half of the volume of the room? …for the energy expelled in the exhaust from a car to spontaneously reform into the chemical energy of the fuel? …to return to a cup of coffee left on the table and find it hotter than when you had first poured it from the coffee pot?

2nd Law of Thermodynamics It is impossible to transfer energy from a body at a lower temperature to one at higher temperature without doing work on the system -or- It is impossible to extract energy from a hot reservoir and transfer this entirely into work. Both wordings sum up that this law relates turning energy into work (1st law is about work transforming into energy)

Entropy (S) ∆𝑆= ∆𝑄 𝑇 A measure of the disorder of a system Units of Entropy (S)  J·K-1 Reversible Process one in which the system will return to its original state Isothermal processes are reversible Irreversible Process one in which the system will not return to its original state ∆𝑆= ∆𝑄 𝑇

Sample Problem 0.20 kg of ice at 0.0°C melts. The specific latent heat of fusion of water is 3.34 x 105 J·kg-1 . Calculate the change in entropy of the ice as it melts.