Consider the following rigid container where an amount of ideal gas initially at a temperature T and pressure P is equally divided by a moveable and thermally insulated partition of negligible size and mass. There are N moles of gas on each side of the partition and Cy= R. Assume the left side is heated until the temperature reaches some multiple m of the initial temperature; i.e., mT, while the right side remains at T . moveable & insulating Q P,T,N T→ mT Vf.LHS (a) Show that the final volume of the left hand side, VLHS is given by the following expression. (Hint: note that the pressures of the left and right sides, although changing throughout the process, are always equal to one another.) P,T,N W. T→T by LHS (b) Show that the work done by the left hand side, WB 2mNRT (1+m)P BY,LHS is given by: = NRT In ¹ (c) Show that the heat taken in by the left hand side, Qin,LHS, is given by: Qin, LHS = NRT [³(m-1) + In ¹+™] (d) Show that the heat taken in by the right hand side, Qin,RHS is given by: Qin,RHS =- W by,LHS= NRT In

Consider the following rigid container where an amount of ideal gas initially at a temperature T and pressure P is equally divided by a moveable and thermally insulated partition of negligible size and mass. There are N moles of gas on each side of the partition and Cy= R. Assume the left side is heated until the temperature reaches some multiple m of the initial temperature; i.e., mT, while the right side remains at T . moveable & insulating Q P,T,N T→ mT Vf.LHS (a) Show that the final volume of the left hand side, VLHS is given by the following expression. (Hint: note that the pressures of the left and right sides, although changing throughout the process, are always equal to one another.) P,T,N W. T→T by LHS (b) Show that the work done by the left hand side, WB 2mNRT (1+m)P BY,LHS is given by: = NRT In ¹ (c) Show that the heat taken in by the left hand side, Qin,LHS, is given by: Qin, LHS = NRT [³(m-1) + In ¹+™] (d) Show that the heat taken in by the right hand side, Qin,RHS is given by: Qin,RHS =- W by,LHS= NRT In

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

Properties of Pure Substances

A substance with fixed chemical composition throughout is called a pure substance like water, air, and nitrogen. A pure substance does not have to be a single element or compound. A mixture of two or more phases of a pure substance is also a pure substance as long as the chemical composition is the same for all phases. These substances mainly have a constant/ uniform composition. The substances also have fixed boiling and melting points. A pure substance takes part in a chemical reaction to form predictable products.

Question

solve a-d

Consider the following rigid container where an amount of ideal gas initially at a
temperature T and pressure P is equally divided by a moveable and thermally insulated
partition of negligible size and mass. There are N moles of gas on each side of the partition and
Cy=R. Assume the left side is heated until the temperature reaches some multiple m of the
initial temperature; i.e., mT, while the right side remains at To.
moveable & insulating
PO,T,N
T→ mT
Vf. LHS
(a) Show that the final volume of the left hand side, VHS is given by the following expression.
(Hint: note that the pressures of the left and right sides, although changing throughout the process,
are always equal to one another.)
W.
P,T,N
by,LHS
T→To
(b) Show that the work done by the left hand side, W , is given by:
BY,LHS
=
2mNRT
(1+m)P
NRT In ¹
(c) Show that the heat taken in by the left hand side, Qin, LHS, is given by:
Qin, LHS = NRT [(m-1) + In¹″]
(d) Show that the heat taken in by the right hand side, Qin,RHS is given by:
Qin, RHS
=-W.
by LHS
= NRT ln ₁²m

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