The discussion centers on the relationship between derivatives and pressure change in the context of a P(V) equation. It establishes that while derivatives represent rates of change, the interpretation depends on the differentiation variable. Specifically, taking the derivative of a P(V) equation with respect to volume yields the rate of change of pressure, not a direct equation for pressure change. The conversation emphasizes the importance of understanding the differentiation variable in determining the meaning of the derivative.
PREREQUISITESStudents and professionals in physics, engineering, and thermodynamics who seek to deepen their understanding of pressure-volume relationships and the application of calculus in these contexts.
What is your definition of an "equation for change in pressure?"JoeyBob said:Homework Statement:: N/A
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I know the integral of a P(V) eqn gives an eqn for work.
I was wondering if taking the derivative of a P(V) eqn gives an eqn for change in pressure?
Gives rate of change.Chestermiller said:What is your definition of an "equation for change in pressure?"
No, the derivative of velocity with respect to time is acceleration. What you differentiate with respect to is important. For example, there are situations where velocity is given as a function of position. The derivative of such a velocity function is not acceleration.JoeyBob said:For instance, if you take the derivative of velocity, you get acceleration, which is the rate of change of velocity.
So it would be rate of change with respect to volume?Orodruin said:No, the derivative of velocity with respect to time is acceleration. What you differentiate with respect to is important. For example, there are situations where velocity is given as a function of position. The derivative of such a velocity function is not acceleration.
Derivatives are rates of change with respect to the differentiation variable, but depending on what the differentiation variable is, the interpretation may vary.