# Change in internal thermal energy.

#### bbhill

Q: 20 J of heat energy is added to an ideal gas while -40J of work is done BY the same gas. The total change in internal thermal energy of the system is what?

Equations I used: $$\Delta$$Eth = Heat + Work
$$\Delta$$Eth = Heat - Ws

This was a problem on a recent physics test I took and I said the answer was 60J. However, my instructor insists that the correct answer is -20J. He says that -40J of work is energy leaving the gas irregardless of whether the gas is doing the work or the environment is doing the work. I don't see how this is possible. My reasoning is that (-40J) of work is done by the gas = 40J of work done ON the gas. Thus, $$\Delta$$Eth= 20 J + 40J.

Can anyone enlighten me on why this is?

Thanks a lot!

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#### Mapes

Homework Helper
Gold Member
I'm on your side. Essentially, the question contains a double negative (a negative amount of exiting energy) which your instructor is interpreting as a negative amount and you are interpreting as a positive amount.

Or look at it this way: most people would take the opposite statement, "40J of work is done by a gas," to mean that 40J of energy left the system. Your instructor is claiming, then, that replacing "40J" with "-40J" in the above sentence makes no difference, which is illogical.

#### Andrew Mason

Homework Helper
You are right. The convention is to write the first law as:

dU = dQ - dW; where dQ is the heat flow INTO the gas and dW is the work done by the gas.

If you are using that convention, a negative work term means that positive work is being done ON the gas so it increases internal energy.

As Mapes noted, if the question had stated that +40J of work is done by the gas, then the change in internal energy would be dQ - dW = 20 - 40 = -20J. So it cannot be the same result if -40J is done by the gas.

Your teacher may be confusing Q with work. Work is not something that "flows" into or out of the gas. That is the case with Q (at least the model on which thermodynamics is based) but not W. Work is only done ON or BY the gas.

AM

#### bbhill

Yeah, these are the same things I told my professor, but he stood firm on his answer. I guess I'll let it slide for now and if my grade is affected at the end of the semester I'll look back into it.

Thanks

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