A chemical process in which heat is absorbed.
A change in which q=30 J, w=44 J.
A process in which a system does work on its surroundings with no change in q.
A process in which work is done on a system and an equal amount of heat is withdrawn.

In how many of these cases does the internal energy of the system decrease? (0,1,2,3,4)

Number of cases where internal energy of system decreases = 1

Explanation:

According to first law of thermodynamics-

                                   

where, , q and w represents change in internal energy, heat exchanged and work done respectively.

When heat is absorbed (q > 0), will also increase.When q = 30 J and w = 44 J, = (30+44) J = 74 J (positive). So, internal energy of system increases.When q = 0 and system does work on its surroundings (w < 0), < 0 (negative). So, internal energy of system decreases.When work id done on system (w > 0) and heat is withdrawn (q < 0) by an equal amount (w = -q), . So, internal energy does not change.

So, number of cases where internal energy of system decreases = 1

You know how the first one if filled up like the objects do the same but with the other categories