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One way to think why heat and work is using this analogy. Suppose that you and your friend are trying to reach a mountain elevation of 1100 m and are at the same initial starting point, lets say at 150 m elevation. You may decide to walk it while your friend opts to take a bus. Then you both compare how much energy was spent using your particular method of travel. One will notice that the person who walked spent way more energy. There are two levels of work presented in this case but it all depends on the path you take to get to the final state in this case the mountain.
State functions simply observe your conditions at that current moment, but in the case of work and heat, the efficiency of each reaction or how it is carried out can determine its value, meaning that you must take into account the entire pathway.
work can't be a state function because it is proportional to the distance an object is moved, which depends on the path used to go from the initial to the final state and thus if work isn't a state function, then heat can't be a state function either because according to the first law of thermodynamics, the change in the internal energy of a system is equal to the sum of the heat and the work transferred between the system and its surroundings.
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