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My TA gave an example where an ice cube was dropped into water in an adiabatic container, and used the equation q=n*detaH(fusion) for the heat to melt and added that to the heat to melt, to find the heat of the system. I was confused on where that equation came from and why exactly we have to add it to find the total value for q of the system.
q=n*detaH(fusion) represents the enthalpy of fusion multiplied by number of mols of ice present. It refers to the heat associated with melting that many mols of ice (n). Since melting ice requires heat, the ice is taking energy from the water, and thus is conferring a temperature change in the water, which can be calculated by . Note that the ice is gaining energy, and that the water is losing energy, and is equal to 0.
An adiabatic system means that all heat within the system remains, so there is no transfer from the adiabatic system to it's surroundings. Concerning the melting of ice, you must use the H(fusion) (kj/mol) and multiply that by moles. If given grams, you divide by the molar mass of water. This way all of your units cancel out and you are left with kj, which describes the heat needed for that particular phase change. You should keep in mind that a phase change from solid to liquid shouldn't require as much energy as a phase change from liquid to vapor.
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