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(a) The van van der Waals equation for $ n $ moles of a gas is$ (P + \frac {n^2 a}{V^2})(V - nb) = nRT $where $ P $ is the pressure, $ V $ is the volume, and $ T $ is the temperature of the gas. The constant $ R $ is the universal gas constant and $ a $ and $ b $ are positive constants that are characteristic of a particular gas. If $ T $ remains constant, use implicit differentiation to rind $ dV/dP. $ (b) Find the rate of change of volume with respect to pressure of 1 mole of carbon dioxide at a volume of $ V = 10L $ and a pressure of $ P = 2.5 $ atm. Use $ a = 3.592 L^2 -atm/mole^2 $ and $ b = 0.04267 L/mole, $

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(a) $ d V / d P=\frac{(n b-V) V^{3}}{2 n^{3} a b+P V^{3}-n^{2} a V} $(b) -4.04

00:39

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Derivatives

Differentiation

Missouri State University

Oregon State University

Harvey Mudd College

Baylor University

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

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(a) The van van der Waals…

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(a) The van der Waals equa…

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The van der Waals equation…

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The $ \textit{van der Waal…

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At high gas densities, t…

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