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.
The derivative of a P(V) equation is the mathematical expression that represents the rate of change of pressure with respect to volume.
The derivative of a P(V) equation is calculated by taking the limit as the change in volume approaches 0 of the ratio of the change in pressure to the change in volume.
Yes, the derivative of a P(V) equation can be used to determine the change in pressure. The derivative represents the instantaneous rate of change of pressure, so by plugging in a specific volume value, the resulting derivative value will give the change in pressure at that particular volume.
No, the derivative of a P(V) equation is not the same as the equation for change in pressure. The derivative gives the instantaneous rate of change, while the equation for change in pressure gives the overall change in pressure over a given range of volume.
Yes, the derivative of a P(V) equation can be used to predict the behavior of a gas. By analyzing the shape of the derivative curve, one can determine how pressure will change as volume changes and make predictions about the behavior of the gas.