The discussion revolves around the relationship between derivatives and pressure in the context of a pressure-volume (P(V)) equation. Participants explore whether taking the derivative of such an equation yields an expression for the change in pressure.
The discussion is active, with participants providing insights into the nature of derivatives and their interpretations. There is a focus on understanding how the differentiation variable affects the outcome, particularly in relation to pressure and volume.
Some participants express uncertainty regarding the definition of change in pressure and how it relates to the differentiation of the P(V) equation. The conversation reflects a lack of consensus on the interpretation of derivatives in this context.
What is your definition of an "equation for change in pressure?"JoeyBob said:Homework Statement:: N/A
Relevant Equations:: N/A
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.