If we added heat (Q) to the, and we knew this resulted in an increase of internal energy (U) of + 15, what would the change in work (W) have to be in order for the equation to balance.

The question is incomplete, here is the complete question:

If we added 10 J of heat (Q) to the system, and we knew this resulted in an increase of internal energy (U) of +15 J, what would the change in work have to be in order for the equation to balance.

The work done for compression is +5 J

Explanation:

According to first law of thermodynamics:

where,

q = heat released or absorbed = +10 J  

When heat is added, it is getting absorbed and sign will be positive and when heat is removed, it is getting released and sign will be negative

dU = internal energy = +15 J

W = work done

Putting values in above equation, we get:

Sign convention of work:

Work done for expansion process is taken as negative and work done for compression is taken as positive.

Hence, the work done for compression is +5 J

since the atomic number is the number of protons in the nucleus, as we move to the left on the periodic table, the electrostatic pull between the nucleus and the valence electron shell decreases. as we move down a group (vertical column), the valence shell energy level gets further and further from the nucleus.