Answer :
Final answer:
In thermodynamics, work done on the system is considered negative. Thus, based on the first law of thermodynamics, the correct statement is '2) The - sign should be replaced by a - sign because (-F_T dL) is the work'. This negative sign denotes that the work is done on the system.
Explanation:
Looking at the identity dU = TdS - F_T dL that you're asking about, we notice that the negative sign between TdS and F_T dL is important. This area is a part of thermodynamics, where dU is a small change in internal energy, TdS is the heat added to the system, and F_T dL is the work done on the system. However, the sign convention is such that work done on the system is negative, and work done by the system is positive.
Therefore, the correct statement among the options given would be '2) The - sign should be replaced by a - sign because (-F_T dL) is the work'. The negative sign shows that the work is done on the system, which is consistent with the given equation in the context of the first law of thermodynamics.
As an example, consider the situation where a force F is applied on an object causing it to move a distance d in the direction of the force. According to the definition of work, work done (W) = F.d. Here the direction of the force and displacement are the same, so the cos0 = 1. Therefore, W = Fd. But since the work is done on the system, by convention, in thermodynamics, this work would be specified with a negative sign, i.e., W = - Fd.
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