What is the relationship between net work and net heat flow for a gas?

[brake4country]

Homework Statement

The net work done on a certain gas is 55J, and the net heat flow into the gas is -23J. What is the net work done by the gas?

Homework Equations

U = q + w

The Attempt at a Solution

This problem seems very conceptual so I didn't use the formula above. I just deduced from this question that if the work done on a gas is 55J, then the work done by the gas is -55J. This is the correct answer but I got thrown off by the -23 J of net heat flow. What does this -23 really mean if the work done by the gas (-55J) is conserved?

 

[James Brady]

The first law of thermodynamics is usually expressed as Δu = q - w. Where energy put into the system is considered positive and work put into the system is considered negative. I don't know what convention your textbook is using, but if the above equation you posted is from your textbook, then heat in is considered positive and work in is considered positive.

All that -23J means is that 23 joules of energy went out of the system. In this case, nothing is really "conserved", it's just +55 Joule done on the system = -55 Joule done by the system and -23 Joule heat into the system = 23 Joule heat out of the system. This law is really useful when considering "steady state" operation of systems where ΔU = 0, that's where you will need to do energy balances.