• Keine Ergebnisse gefunden

Universität Stuttgart

N/A
N/A
Info
Herunterladen
Protected

Academic year: 2021

Aktie "Universität Stuttgart"

Copied!
1
0
0

Wird geladen.... (Jetzt Volltext ansehen)

Jetzt herunterladen ( 1 Seite )

Volltext

(1)

Universität Stuttgart

Fakultät 8, Fachbereich Physik

Prof. Dr. Rudolf Hilfer Tillmann Kleiner

Advanced Statistical Physics, SS 2017 Sheet 3

Problem 1: (4 points)

Show that the two formulations of the Second Law are equivalent. For review, the two formulations are:

Clausius: Heat cannot go from a colder body to a warmer body unless there is simul- taneously another change related to it.

Planck - Thomson: It is impossible to construct a periodically working machine that does nothing else but lift a weight (do work) and cool a heat reservoir. (Such a machine is called perpetuum mobile of second kind.)

Problem 2: (4 points)

a) Show that there is no machine between two fixed temperature heat reservoirs that is more efficient than the Carnot cycle.

b) Show that all reversible machines between two reservoirs have the same efficiency.

Problem 3: (4 points)

a) Consider a thermodynamic system with internal energy U = U (S, V, N ). Show that T =

∂U∂S

is intensive given that U , S, V and N are extensive.

b) Suppose two systems, one with internal energy U

1

(S

1

, V

1

, N

1

) and another with internal energy U

2

(S

2

, V

2

, N

2

) are allowed to exchange heat (but not work or mass) through a fixed wall. Show that the second law implies that this exchange of heat cannot decrease the total entropy S

1

+ S

2

.

Hint: In Problem 1 assume that there is a process or a machine contradicting one of the two statements. Couple it with a Carnot cycle to construct a composite process or machine which contradicts the other of the two statements. Note, that a Carnot cycle may be driven in both directions, converting heat into work or work into heat. Proceed similary for Problem 2.

Deliver your hand-written solutions at the beginning of the lecture on Friday, May 5th.

Referenzen

Jetzt herunterladen ( PDF - 1 Seite - 108.38 KB )

ÄHNLICHE DOKUMENTE

A Sample State Machine

Till Mossakowski Semantics of UML state machines.. .}, {Idle}) In particular, PINEntered occurs both as a state and as a.. completion event in the

It is two and a half minutes to midnight

2015 IT IS 3 MINUTES TO MIDNIGHT Unchecked climate change, global nuclear weapons modernizations, and outsized nuclear weapons arsenals pose extraordinary and undeniable threats

Is anti-Semitism a homogeneous construct?

Since each of the four subscales defines more or less the same rank order between the identified classes of participants, we may conclude that each of the facets – ruling off the

This is a

The validation process should include a plausibility check of the driving meteorological inputs, of soil and stand variables, and of the measured data used for validation, which

(a) Show that M∩(−M) is an ideal of A

Fachbereich Mathematik und

1. Show that a space is T

Use also the facts that R with the usual topology is second countable and that every family of pairwise disjoint nonempty open sets must be countable.)7. Let (X, τ ) be the

Some day we will build a think- ing machine. It will be a truly intelligent machine. One that can see and hear and speak. A machine that will be proud of us.

the top of the list: building a computer ca- pable of a teraflop-a trillion floating- point operations per second. Not surprisingly, Thinking Machines 63.. had an inside track

Is it a Wave? Is it a Particle?

Indivisible (single) particles à no coincidences (Elementary) Particles explain:. •  No inner