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I had written down the equation from lecture which showed how to calculate the sum of an infinite number of steps by using an integral with an external pressure, but in the end Dr. Lavelle reached the equation w= -P*Delta V, so is the integral something we will be using or was it more to derive the equation in the end? Thank you!
I feel that he used the integral as a conceptual device to be able to reveal the idea he was trying to portray with the sum of infinitesimal changes in volume. Under constant pressure, P can be pulled out of the integral as a constant, and the change in V will be left as the product of the integral of dv. Thus we get w=-p(delta v)
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