A small, easy algebraic question about the First Law of Thermo for SISO

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SUMMARY

The discussion centers on the algebraic manipulation of the First Law of Thermodynamics for a Single Input Single Output (SISO) system, specifically the equation Q(dot) - Ws(dot). The user seeks clarification on the placement of terms in the equation, questioning why it is not represented as W - Q. Through a series of substitutions and simplifications, the user demonstrates that Q(dot) - Ws(dot) can be represented as u, leading to the equation u + v - w = 0. This manipulation ultimately clarifies the relationship between heat transfer and work done in thermodynamic processes.

PREREQUISITES
  • Understanding of the First Law of Thermodynamics
  • Familiarity with algebraic manipulation and substitution
  • Knowledge of thermodynamic terms such as Q(dot) and Ws(dot)
  • Basic concepts of Single Input Single Output (SISO) systems
NEXT STEPS
  • Study the derivation of the First Law of Thermodynamics in detail
  • Learn about the implications of Q(dot) and Ws(dot) in thermodynamic cycles
  • Explore examples of SISO systems in thermodynamic applications
  • Investigate the relationship between enthalpy, kinetic, and potential energy in thermodynamics
USEFUL FOR

This discussion is beneficial for students of thermodynamics, educators teaching the First Law, and professionals working with SISO systems in engineering and physics.

FermiParadox
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O_o. I know this is a really stupid question, but how the heck did the Q - W get to the other side of the equation? Shouldn't it be W - Q? I'm going to feel really stupid when I hear the answer, I'm sure, and I'm already done with the class so it's ultimately irrelevant, but I'd love to know.
 
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Since you don't have an expert answer yet, I will try for an easy one. I am sure the experts will shoot me down if my thinking is wrong...

Q(dot) - Ws(dot) is still on the left in the final equation.

Substitute each term for a letter. Let us use u, v and w. Put a pair of brackets round Q(dot) - Ws(dot) and that is u.

Then you start with u + v - w = 0

Adding w gives u + v = w

Subtracting v gives u = w - v

u still equals Q(dot) - Ws(dot)

(The term on the right hand side has been simplified from w - v for your final equation).
 
Last edited:
Bandit127 said:
Since you don't have an expert answer yet, I will try for an easy one. I am sure the experts will shoot me down if my thinking is wrong...

Q(dot) - Ws(dot) is still on the left in the final equation.

Substitute each term for a letter. Let us use u, v and w. Put a pair of brackets round Q(dot) - Ws(dot) and that is u.

Then you start with u + v - w = 0

Adding w gives u + v = w

Subtracting v gives u = w - v

u still equals Q(dot) - Ws(dot)

(The term on the right hand side has been simplified from w - v for your final equation).

Dude, that makes total sense. It simultaneously explains where the "change in" signs on enthalpy and kinetic and potential came from. Thanks a ton.
 

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