In a second process on the same kind of system, heat transfer of 150.0…

Question

In a second process on the same kind of system, heat transfer of 150.00 J leaves the system while 159.00 J of work is done on the system. Compared with the 9.00 J increase in internal energy found for an earlier two-step process with completely different heat and work values, what is true of the internal energy change here?

Accepted Answer

C. It is the same 9.00 J increase, even though Q and W differ

1. Here Q = -150.00 J (heat leaves the system) and W = -159.00 J (work is done on the system).
2. Applying ΔU = Q - W gives ΔU = -150.00 J - (-159.00 J) = 9.00 J.
3. This matches the 9.00 J found for the earlier process even though the individual values of Q and W are completely different.
4. The source highlights this as a demonstration that ΔU is independent of path: only the net change matters, not the route taken to it, so options B and D are wrong to assume more heat or work automatically changes the result.
5. Comparing joule values across two processes measured in the same unit is a normal calculation, so option A's objection does not apply.
_Source: OpenStax College Physics (CC BY 4.0), Ch 15 "Thermodynamics", section 15.1 The First Law of Thermodynamics_

Answer

It cannot be compared because the two processes use different units

Answer

It must be smaller, since less heat transfer occurred overall

Answer

It must be larger, since more work was involved overall