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The limitation of the first law of thermodynamics is that it cannot tell us the direction of the process.
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Answer
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Hint: The first law of thermodynamics states the total energy of the universe remains constant, although it may undergo a transformation from one form to another. But it does not tell about the spontaneity or feasibility of the process.

Complete answer:
The first law of thermodynamics states that:
Energy can neither be created nor destroyed although it may be converted into from one form to another or states the total energy of the universe remains constant, although it may undergo a transformation from one form to another or the energy of an isolated system is constant.
All these definitions correspond to the state function of the process, which remains the same in all conditions.
A very big drawback of the first law of thermodynamics is that it scarcely indicates that in any of the process, there exists an exact equivalence among the different forms of energy involved in it but it provides no information concerning the spontaneity or feasibility of the process, i.e., whether the process is possible or not or we can say that in which direction the process will occur, forward direction or backward direction.
For example, the first law does not point whether the heat flow is possible from a cold part to a hot part or not. All that tells us that if this process occurred, the heat gained by one end would be exactly equal to that lost by the other end.
Hence, the statement that the limitation of the first law of thermodynamics is that it cannot tell us the direction of the process is true.

Note:
The other limitation of the first law of thermodynamics is that it does not tell whether gas can diffuse from lower pressure to high pressure or water can itself run uphill. This law is not applicable to microscopic material like an individual atom or molecule.