How Does the Definition of Work Affect the First Law of Thermodynamics Equation?

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Homework Help Overview

The discussion revolves around the definition of work in the context of the First Law of Thermodynamics and its implications for energy transfer in thermodynamic systems, specifically gases. Participants are examining how different definitions of work affect the equations used to describe changes in internal energy.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are exploring the nuances of the definition of work, particularly who is doing the work and on whom it is done. There is a focus on the variations in the First Law of Thermodynamics as presented in different textbooks, specifically the signs associated with work in the equations.

Discussion Status

There is an ongoing exploration of the definitions and implications of work in thermodynamic equations. Some participants are seeking clarification on which equation corresponds to work done on the gas and the reasoning behind it. The discussion reflects a productive engagement with the material, though no consensus has been reached yet.

Contextual Notes

Participants are noting the importance of careful language and definitions in thermodynamics, as well as the potential for confusion arising from different textbook conventions regarding the sign of work in the First Law of Thermodynamics.

Nick tringali
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Homework Statement
I picked choice A but the Answer is choice B. The book literally states that when work is done on the system work is negative. I get that when it’s Adiabatic the equation simplifies to U=-W making it U=-(-W). Is this like a trick question? Why would the book tell me that when work is done on the system work is negative then also ask a question and state it’s actually positive. Hope this question makes sense.
Relevant Equations
Delta U= Q-W
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Hi @Nick tringali.

You have to be very careful when thinking about the direction of energy-transfer when work is done (on something by something else).

Your textbook link says "... W is the work done by the system" [my underlining].
But the question is about "the work done on the gas" [my underlining; and of course 'the gas' is 'the system' here].
 
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Yes, one needs to be careful about the preposition and be careful about who does the work and on whom work is done. It doesn't help that the first law appears as ##\Delta U=Q+W## in some textbooks and as ##\Delta U=Q-W## in others. Both are correct depending on the definition of ##W## in the textbook. As usual, ##\Delta U## is the change in internal energy and ##Q## is the heat that enters the gas.

To Nick tringali: Can you tell in which equation ##W## stands for "work done on the gas" and why? If so, then you understand what is going on here.
 
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kuruman said:
Yes, one needs to be careful about the preposition and be careful about who does the work and on whom work is done. It doesn't help that the first law appears as ##\Delta U=Q+W## in some textbooks and as ##\Delta U=Q-W## in others. Both are correct depending on the definition of ##W## in the textbook. As usual, ##\Delta## is the change in internal energy and ##Q## is the heat that enters the gas.

To Nick tringali: Can you tell in which equation ##W## stands for "work done on the gas" and why? If so, then you understand what is going on here.
I would say that U= Q+W equation is where W stands for work done on the gas. When work is done on the gas it increases the internal energy so +W being work done on the gas would make sense . Right?
 

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