The internal energy of a system changes because the system gains 160 j of heat and performs 309 j of work. in returning to its initial state, the system loses 106 j of heat. during this return process, what work is involved, and is the work done by the system or on the system?

w=255

Explanation:

The change in internal energy is given by the first law:

ΔE = Q - w

where ΔE is the change in internal energy of the system

q is the heat added to the system

w is the work done *by* the system on the surroundings

So, for the first phase of this process:

ΔE = Q - w

Q=160J

w=309J

ΔE = 160J - 309J = -149J

To bring the system back to its initial state after this, the internal energy must change by +149J (the system myst gain back the 149 J of energy it lost).  We are told that the system loses 106 J of heat in returning to its initial state, so the work involved is given by:

ΔE = Q - w

+149J = -106J - w

255J = -w

w = -255J

0.19 m/s and 0.45 m/s