On a counter is a glass of water with ice cubes floating in it. You measure the temperature and find it to be 0 C. Would the temperature of the water change if you were to add more ice cubes to the glass?
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Since the melting process is isothermal, there is no temperature change in the system as long as there are some ice floating in the water. Adding more ice to the glass then will not affect the temperature of the system.
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