Which statement is always true if ΔU sys is always negative?

a) q = w
b) +q>–w
c) -w> +q
d) +w>-q

NVM that answer on top^^^

-w > +q

delta U = heat in - work out

delta U = Q - W in physics
HOWEVER chem texts sometimes use
delta U = Q + W
with W = work IN so maybe that is what you have here.
in that case if delta U is - then
Q < -W heat in less than work out which is c)

Well, well, well! ΔU sys being always negative means that the system's internal energy is constantly decreasing. Now, regarding your options:

a) q = w: Sorry, that won't always hold true. The heat transfer (q) and work done (w) on the system can have different values, so this one is a no-go.

b) +q > –w: Ah, close but no cigar. Even though the magnitude of q might be greater than the magnitude of -w, we can't say for sure that it will always be the case.

c) -w > +q: Now we're cooking! This option says that the magnitude of -w is greater than the magnitude of +q, and since ΔU sys is always negative, this statement holds true. Well done!

d) +w > -q: Nope, not gonna happen. This option implies that the magnitude of +w is greater than the magnitude of -q, but we can't make such a definitive claim.

So, the answer is c) -w > +q. Good job!

To determine which statement is always true if ΔUsys is always negative, let's first understand the meaning of each term involved.

ΔUsys represents the change in internal energy of the system. If the value of ΔUsys is always negative, it means that the system is losing energy.

Now let's analyze each statement:

a) q = w: This statement refers to the relationship between heat (q) and work (w). However, it does not necessarily pertain to the change in internal energy of the system. Therefore, we cannot determine whether it is always true based solely on ΔUsys being negative.

b) +q > -w: This statement suggests that the magnitude of heat gained by the system (+q) is greater than the magnitude of work done on the system (-w). Although it is a possibility, it is not always true when ΔUsys is negative. The relative magnitudes of heat and work cannot be determined without additional information.

c) -w > +q: This statement implies that the magnitude of work done on the system (-w) is greater than the magnitude of heat gained by the system (+q). Again, like option b, this relationship is not always true solely based on ΔUsys being negative.

d) +w > -q: This statement suggests that the magnitude of work done by the system (+w) is greater than the magnitude of heat lost by the system (-q). When ΔUsys is negative, it indicates that the system is losing energy. In such cases, it is always true that the magnitude of work done by the system is greater than the magnitude of heat lost. Therefore, option d is the correct choice.

In summary, the statement that is always true if ΔUsys is always negative is option d) +w > -q.

+w>-q