Hi Guys! I have a confusion which I hope you can help clear up. The mathematical expression of the first law of thermodynamics can be stated as δu=Q+W where u is the internal energy of the system, Q is the heat added(or taken from) to the system and W is the work done by or on the system. If I lift a glass of water to a certain height, the internal energy is unaffected correct? But if we refer to the equation before, work is being done on the system (changing its gravitational potential ), so why doesn't this form of work done qualify to appear in the system? ( My hunch is that for this form, the system has to include the cup and the zero gravitational potential reference ). Next question, If we would freeze a cup of water at a constant temperature, does the internal energy change? From the equation, heat is taken away from the system, but I am not too certain as to any work is done by the system. So, δu most likely <0 Alternatively, u = sum of molecular kinetic and potential energy. since temperature is constant, kinetic energy is constant, but I am sure that potential energy has increased since water molecules form more bonds with and come close to each other in the solid state. Here, I would think that δu>0. Then, I seem to contradict myself LOL. Perhaps someone can point out where I got my assumptions wrong? Thank you for your time, have a great day.