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New Trolls

New Trolls (1966)

New Trolls est le nom d’un groupe musical italien de Rock progressif italien formé à Gênes en 1967 connu pour leur fusion de rock et de musique classique. Leur histoire est remplie de changements musiciens, de nom de groupe et de rivalités entre les membres du groupe.

La bande s’est formée au milieu des années 1960 quand les musiciens Vittorio De Scalzi, Nico Di Palo, Mauro Chiarugi, Giorgio D’Adamo et Gianni Belleno décident de former le groupe « New Trolls », d’après le nom d’un précédent groupe de l’un d’entre eux :« Trolls ».

Après une première série de concerts dans les clubs locaux, New Trolls ont gagné en popularité au point qu’ils ont été choisis pour être des soutiens pour les Rolling Stones lors de la tournée italienne. Peu après glass reusable water bottles, ils sortent leur premier single, Sensazioni (1967). À l’époque, le groupe a été parmi les meilleurs dans son genre en Italie et le guitariste Nico Di Palo s’inspirant de Jimi Hendrix était l’un des premiers héros de guitare italien. Leur premier album, Senza orario Senza bandiera sorti en 1968 a bénéficié des paroles écrites pour par le chanteur-compositeur Fabrizio De André.

Un deuxième album, simplement intitulé New Trolls est suivi deux ans plus tard (1970) par une compilation de leurs singles. À la fin de la même année les New Trolls sont confrontés à leur premier changement, quand Mauro Chiarugi quitte le groupe metal meat tenderizer. Les autres membres continuent en quatuor.

De nombreux changements interviennent tout au long de la vie du groupe.

Table of thermodynamic equations

This article is a summary of common equations and quantities in thermodynamics (see thermodynamic equations for more elaboration). SI units are used for absolute temperature, not Celsius or Fahrenheit.

Many of the definitions below are also used in the thermodynamics of chemical reactions.





τ



=



k



B






(






U



/







S


)




N








{\displaystyle \tau =k_{B}\left(\partial U/\partial S\right)_{N}\,\!}






1



/



τ



=


1



/




k



B






(






S



/







U


)




N








{\displaystyle 1/\tau =1/k_{B}\left(\partial S/\partial U\right)_{N}\,\!}






S


=




(






F



/







T


)




V








{\displaystyle S=\left(\partial F/\partial T\right)_{V}\,\!}


,





S


=




(






G



/







T


)




N


,


P








{\displaystyle S=\left(\partial G/\partial T\right)_{N,P}\,\!}






P


=








(






U



/







V


)




S


,


N








{\displaystyle P=-\left(\partial U/\partial V\right)_{S,N}\,\!}


component i in a mixture)






μ




i




=




(






F



/








N



i




)




T


,


V








{\displaystyle \mu _{i}=\left(\partial F/\partial N_{i}\right)_{T,V}\,\!}


, where F is not proportional to N because μi depends on pressure.






μ




i




=




(






G



/








N



i




)




T


,


P








{\displaystyle \mu _{i}=\left(\partial G/\partial N_{i}\right)_{T,P}\,\!}


, where G is proportional to N (as long as the molar ratio composition of the system remains the same) because μi depends only on temperature and pressure and composition.






μ




i





/



τ



=






1



/




k



B






(






S



/








N



i




)




U


,


V








{\displaystyle \mu _{i}/\tau =-1/k_{B}\left(\partial S/\partial N_{i}\right)_{U,V}\,\!}


The equations in this article are classified by subject.

For an ideal gas





W


=


k


T


N


ln






(



V



2





/




V



1




)






{\displaystyle W=kTN\ln(V_{2}/V_{1})\,\!}






Δ



W


=


p


Δ



V


,



Δ



Q


=


Δ



U


+


p


δ



V






{\displaystyle \Delta W=p\Delta V,\quad \Delta Q=\Delta U+p\delta V\,\!}






Δ



W


=


0


,



Δ



Q


=


Δ



U






{\displaystyle \Delta W=0,\quad \Delta Q=\Delta U\,\!}


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; height:2.676ex;” alt=”\Delta W = 0, \quad \Delta Q = \Delta U\,\!”>






T



1





V



1




γ







1




=



T



2





V



2




γ







1








{\displaystyle T_{1}V_{1}^{\gamma -1}=T_{2}V_{2}^{\gamma -1}\,\!}






Δ



W


=









V



1







V



2






p



d



V






{\displaystyle \Delta W=\int _{V_{1}}^{V_{2}}p\mathrm {d} V\,\!}


Net Work Done in Cyclic Processes





Δ



W


=








c


y


c


l


e





p



d



V






{\displaystyle \Delta W=\oint _{\mathrm {cycle} }p\mathrm {d} V\,\!}










p



1





V



1







p



2





V



2







=






n



1





T



1







n



2





T



2







=






N



1





T



1







N



2





T



2











{\displaystyle {\frac {p_{1}V_{1}}{p_{2}V_{2}}}={\frac {n_{1}T_{1}}{n_{2}T_{2}}}={\frac {N_{1}T_{1}}{N_{2}T_{2}}}\,\!}






n


R


T


ln









P



1





P



2









{\displaystyle nRT\ln {\frac {P_{1}}{P_{2}}}\;}






C



p




=




7


2




n


R





{\displaystyle C_{p}={\frac {7}{2}}nR\;}



(for diatomic ideal gas)






C



V




=




5


2




n


R





{\displaystyle C_{V}={\frac {5}{2}}nR\;}



(for diatomic ideal gas)

Below are useful results from the Maxwell–Boltzmann distribution for an ideal gas, and the implications of the Entropy quantity. The distribution is valid for atoms or molecules constituting ideal gases.

K2 is the Modified Bessel function of the second kind.





P



(


v


)



=


4


π





(




m



2


π




k



B




T





)




3



/



2





v



2





e







m



v



2





/



2



k



B




T








{\displaystyle P\left(v\right)=4\pi \left({\frac {m}{2\pi k_{B}T}}\right)^{3/2}v^{2}e^{-mv^{2}/2k_{B}T}\,\!}


Relativistic speeds (Maxwell-Jüttner distribution)





f


(


p


)


=




1



4


π




m



3





c



3




θ
< thermos intak hydration bottle with meter!– θ –>



K



2




(


1



/



θ



)






e







γ



(


p


)



/



θ







{\displaystyle f(p)={\frac {1}{4\pi m^{3}c^{3}\theta K_{2}(1/\theta )}}e^{-\gamma (p)/\theta }}


where:






P



i




=


1



/



Ω







{\displaystyle P_{i}=1/\Omega \,\!}






Δ



S


=



k



B




N


ln









V



2





V



1






+


N



C



V




ln









T



2





T



1










{\displaystyle \Delta S=k_{B}N\ln {\frac {V_{2}}{V_{1}}}+NC_{V}\ln {\frac {T_{2}}{T_{1}}}\,\!}











E




k









=




1


2




k


T






{\displaystyle \langle E_{\mathrm {k} }\rangle ={\frac {1}{2}}kT\,\!}


Internal energy





U


=



d



f









E




k









=





d



f




2




k


T






{\displaystyle U=d_{f}\langle E_{\mathrm {k} }\rangle ={\frac {d_{f}}{2}}kT\,\!}


Corollaries of the non-relativistic Maxwell–Boltzmann distribution are below.

For quasi-static and reversible processes, the first law of thermodynamics is:

where δQ is the heat supplied to the system and δW is the work done by the system.

The following energies are called the thermodynamic potentials,

and the corresponding fundamental thermodynamic relations or “master equations” are:

The four most common Maxwell’s relations are:







(









T








P





)




S




=


+




(









V








S





)




P




=











2




H








S






P







{\displaystyle \left({\frac {\partial T}{\partial P}}\right)_{S}=+\left({\frac {\partial V}{\partial S}}\right)_{P}={\frac {\partial ^{2}H}{\partial S\partial P}}}






+




(









S








V





)




T




=




(









P








T





)




V




=















2




F








T






V







{\displaystyle +\left({\frac {\partial S}{\partial V}}\right)_{T}=\left({\frac {\partial P}{\partial T}}\right)_{V}=-{\frac {\partial ^{2}F}{\partial T\partial V}}}












(









S








P





)




T




=




(









V








T





)




P




=











2




G








T






P







{\displaystyle -\left({\frac {\partial S}{\partial P}}\right)_{T}=\left({\frac {\partial V}{\partial T}}\right)_{P}={\frac {\partial ^{2}G}{\partial T\partial P}}}


More relations include the following.

Other differential equations are:

where N is number of particles, h is Planck’s constant, I is moment of inertia, and Z is the partition function, in various forms:

Since

Since

(where δWrev is the work done by the system),






λ





n


e


t





=








j





λ




j








{\displaystyle \lambda _{\mathrm {net} }=\sum _{j}\lambda _{j}\,\!}


Parallel








1


λ







n


e


t





=








j





(





1


λ






j




)







{\displaystyle {\frac {1}{\lambda }}_{\mathrm {net} }=\sum _{j}\left({\frac {1}{\lambda }}_{j}\right)\,\!}






η



=



|




W



Q



H






|







{\displaystyle \eta =\left|{\frac {W}{Q_{H}}}\right|\,\!}


Carnot engine efficiency:






η




c




=


1







|





Q



L





Q



H






|



=


1









T



L





T



H










{\displaystyle \eta _{c}=1-\left|{\frac {Q_{L}}{Q_{H}}}\right|=1-{\frac {T_{L}}{T_{H}}}\,\!}






K


=



|





Q



L




W




|







{\displaystyle K=\left|{\frac {Q_{L}}{W}}\right|\,\!}


Carnot refrigeration performance






K



C




=






|




Q



L





|






|




Q



H





|








|




Q



L





|






=





T



L






T



H









T



L











{\displaystyle K_{C}={\frac {|Q_{L}|}{|Q_{H}|-|Q_{L}|}}={\frac {T_{L}}{T_{H}-T_{L}}}\,\!}