what is meant byt the statement, “internal energy is afunction of state”. will the internal energy of a system increase or decrease when work is done on it? write the mathematical statement for the first law of thermodynamics. write the convention used for determination of a sign of work done in this expression.

That means that internal energy change of a system depends only on the final and initial state of the system and not on how the system reaches that state.Suppose you choose two path(one adiabatic and one isothermal)to go from initial state P1,V1,T1 to final state  P2,V2,T2.You know that work done will depend on the path,for adiabatic process work done is different from work done in isothermal process.But internal energy change in both cases are the same because the initial and final states are the same.

When work is done on the system internal energy increases.

The first law can be mathematically written as

dcut(Q)=dU+dcut(W)

dcut is means not perfect differential.

Work done by the system is positive.

Please approve if helped.thank u.