When a gas follows path 123 on the PV diagram in a rectangle shape labeled 1234 cycle, 449 J of heat flows into the system and 179 J of work is done.

What is the change in the internal energy of the system?

* I keep coming up with 270 but this is incorrect. PLEASE HELP :)

To determine the change in the internal energy of the system, we can use the First Law of Thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat (Q) supplied to the system minus the work (W) done by the system:

ΔU = Q - W

In this case, the heat flowing into the system is given as 449 J, and the work done by the system is given as 179 J.

By substituting these values into the equation, we can calculate the change in internal energy:

ΔU = 449 J - 179 J
ΔU = 270 J

Therefore, the change in the internal energy of the system is 270 J.

It seems like you've also arrived at this answer. If you have been consistently coming up with 270 J as the change in internal energy and it is being marked as incorrect, there could be a mistake in the answer key or some additional information that needs to be taken into account. Double-checking your calculations and verifying the given information might help resolve the discrepancy.