Consider that 214 J of work are done on a system, and 293 J of heat are extracted from the system. In the sense of the first law of thermodynamics, what are the values(including algebraic signs) of (a) W, (b) Q, and (C) ∆E_int?

(a) Since work is done on the system, therefore algebraic sign of the work done will be positive and the magnitude of work done is 214 J.
Thus, W = +214 J.
(b) Since heat is extracted from the system, therefore algebraic sign of the heat will be negative and the magnitude of heat is 293 J.
Thus, Q = -293 J.
(c) To obtain internal energy of the system, substitute -293 J for Q and +214 J for W in the equation ΔEint = Q + W,ΔEint = Q + W
= (-293 J) + (+214 J)
= -79.0 J
From the above observation we conclude that, the internal energy of the system would be -79.0 J.