Question

Zustandsgleichung idealer Gase Für cin ideales Gas mit Druck $P$, Volumen $V$ und abso. luter Temperatur $T$ gilt die Zustandsgleichung $P V=c T(c$ eine Konstante). Beweise fur ein 5olches Gas die Beziehung $$ \frac{\partial V}{\partial T} \frac{\partial T}{\partial P} \frac{\partial P}{\partial V}=-1 $$

Name: Problem 10, Chapter 162: Lehrbuch der Analysis
Uploaded: 2023-07-16T23:02:24-08:00
Duration: 2 min 53 s
Channel: Willis James
Description: Zustandsgleichung idealer Gase Für cin ideales Gas mit Druck P, Volumen V und abso. luter Temperatur T gilt die Zustandsgleichung P V=c T(c eine Konstante). Beweise fur ein 5olches Gas die Beziehung (∂V)/(∂T) (∂T)/(∂P) (∂P)/(∂V)=-1

   Zustandsgleichung idealer Gase Für cin ideales Gas mit Druck $P$, Volumen $V$ und abso. luter Temperatur $T$ gilt die Zustandsgleichung $P V=c T(c$ eine Konstante). Beweise fur ein 5olches Gas die Beziehung
$$
\frac{\partial V}{\partial T} \frac{\partial T}{\partial P} \frac{\partial P}{\partial V}=-1
$$

Lehrbuch der Analysis

Harro Heuser 2nd Edition

Chapter 162, Problem 10

Instant Answer

Solved by Expert Willis James

07/16/2023

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We know the equation of state for an ideal gas is given by $PV = cT$, where $c$ is a constant. Show more…

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Zustandsgleichung idealer Gase Für cin ideales Gas mit Druck $P$, Volumen $V$ und abso. luter Temperatur $T$ gilt die Zustandsgleichung $P V=c T(c$ eine Konstante). Beweise fur ein 5olches Gas die Beziehung $$ \frac{\partial V}{\partial T} \frac{\partial T}{\partial P} \frac{\partial P}{\partial V}=-1 $$

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Key Concepts

Ideal Gas Law

The ideal gas law is an equation of state that links pressure, volume, and absolute temperature for an ideal gas. It establishes a linear relationship among these variables, where, under constant conditions, changes in one variable will predictably affect the others. This law simplifies the analysis of gas behavior under various thermodynamic processes and provides a foundational model in the study of gases.

Cyclic Relation of Partial Derivatives

The cyclic relation of partial derivatives is a mathematical principle that applies when three variables are interdependent through an equation of state. It states that the product of three specific partial derivatives, taken in a cyclic order, is equal to -1. This relation is essential in thermodynamics and other fields because it helps relate the sensitivities of different variables to changes in one another, ensuring consistency and closure in implicit differentiation of multivariable systems.

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