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CheMech
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Homework Statement
(a) A certain battery runs a toy truck and becomes partially discharged. In the process, it performs a total of 117J of work on its immediate surroundings. It also gives off 3.0J of heat, which the surroundings absorb No other work or heat is exchanged with the surroundings. Compute q, w, and ∆U of the battery, making sure each quantity has the proper sign.
(b) The same battery is now recharged exactly to its original condition. This requires 210J of electrical work from an outside generator. Determine q for the battery in this process. Explain why q has the sign that it does.
Homework Equations
∆U=q+w
The Attempt at a Solution
The main problem I'm having is determining what sign each quantity is. I know that q is negative if the system loses heat, and positive if heat flows into it. ∆U seems pretty self explanatory: if the system gains total energy, then ∆U is positive. If it loses total energy, then ∆U is negative.
I'm mostly confused with determining the sign of work. In part (a), the problem states that the battery performs 117J of work on its immediate surroundings. I can think of two arguments that explain why work should be positive or negative.
I could see work as positive because the system does positive work on the environment. An analogy could be that it applies a force to the environment, and the environment is affected.
I could see it as negative though because: (1) The system loses energy by performing work (exothermic), hence the negative sign, and (2) As the system performs work on the surroundings, the surroundings perform work on the system. If the system does 117J of work, then -117J of work is done on the system. Like a free body diagram in physics, are we supposed to focus on the work done to the system to determine the correct sign, or are we supposed to focus on the work the system does on the environment?
Any help is greatly appreciated :)
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