(a) Derive the following general relations ᎥᎢ T av (ii) (3)s (ii) (3) др —¿ [T (31), −³], Ср Cv др ᏭᎢ [T(r), -v] ᏭᎢ In each case the quantity on the left-hand side is the appropriate thing to consider for a particular type of expansion. State what type of expansion each refers to. (b) Using these relations, verify that for an ideal gas (T/V) = 0 and (ƏT/ǝp) H = 0, and that (T/V)s leads to the familiar relation PV = constant along an isentrope (a curve

(a) Derive the following general relations ᎥᎢ T av (ii) (3)s (ii) (3) др —¿ [T (31), −³], Ср Cv др ᏭᎢ [T(r), -v] ᏭᎢ In each case the quantity on the left-hand side is the appropriate thing to consider for a particular type of expansion. State what type of expansion each refers to. (b) Using these relations, verify that for an ideal gas (T/V) = 0 and (ƏT/ǝp) H = 0, and that (T/V)s leads to the familiar relation PV = constant along an isentrope (a curve

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

(a) Derive the following general relations
T
(i) (31),
T
U
(ii)
=
av
S
T
(iii)
=
др
др
-r().-]
др
-&T (ST),
Cv
Ꮴ
()()()]
Ср
In each case the quantity on the left-hand
side is the appropriate thing to consider for
a particular type of expansion. State what
type of expansion each refers to.
(b) Using these relations, verify that for an ideal
gas (T/V) = 0 and (T/ǝp) = 0, and
that (T/V)s leads to the familiar relation
pV? = constant along an isentrope (a curve
of constant entropy).

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