Consider a metal rod with the equation of state L- Lo = Lo +a(T – T3) %3D YA

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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2. Consider a metal rod with the equation of state
L- Lo = Lo
+a(T
YA
%3D
Here Lo, Y, A, To, and a are constants,T is the temperature, L is the length,
and F is the tension. Work is given by dW
a) Using the first law and the expression for dU in terms of it partial derivatives
with respect to T and L, show that for this system
-FdL.
(). -). G). (4). -
se,
b) By differentiating the first of these equations with respect to L and the second
with respect to T show that
),
-r(器).
=F-T
ƏT
c) Using the above result and the equation of state, find an expression for
(0/aL). Then, assuming that C. the heat capacity at constant length is a
Constant. find an expression for the internal energy, U, as a function of T and L.
Transcribed Image Text:2. Consider a metal rod with the equation of state L- Lo = Lo +a(T YA %3D Here Lo, Y, A, To, and a are constants,T is the temperature, L is the length, and F is the tension. Work is given by dW a) Using the first law and the expression for dU in terms of it partial derivatives with respect to T and L, show that for this system -FdL. (). -). G). (4). - se, b) By differentiating the first of these equations with respect to L and the second with respect to T show that ), -r(器). =F-T ƏT c) Using the above result and the equation of state, find an expression for (0/aL). Then, assuming that C. the heat capacity at constant length is a Constant. find an expression for the internal energy, U, as a function of T and L.
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