Question

10. Given $du = Tds - pdv$, find a Legendre transformation giving (a) a function $f(T, v)$; (b) a function $h(s, p)$; (c) a function $g(T, p)$. Hint for (c): Perform a Legendre transformation on both terms in $du$. Using $du$ in Problem 10, and the text method of obtaining (11.27), show that $\left(\frac{\partial T}{\partial v}\right)_s = -\left(\frac{\partial p}{\partial s}\right)_v$. (This is one of the Maxwell relations in thermodynamics.)

          10. Given $du = Tds - pdv$, find a Legendre transformation giving
(a) a function $f(T, v)$;
(b) a function $h(s, p)$;
(c) a function $g(T, p)$.
Hint for (c): Perform a Legendre transformation on both terms in $du$.
Using $du$ in Problem 10, and the text method of obtaining (11.27), show that
$\left(\frac{\partial T}{\partial v}\right)_s = -\left(\frac{\partial p}{\partial s}\right)_v$. (This is one of the Maxwell relations in thermodynamics.)

10. Given du = Tds - pdv, find a Legendre transformation giving
(a) a function f(T, v);
(b) a function h(s, p);
(c) a function g(T, p).
Hint for (c): Perform a Legendre transformation on both terms in du.
Using du in Problem 10, and the text method of obtaining (11.27), show that
((∂ T)/(∂ v))s = -((∂ p)/(∂ s))v. (This is one of the Maxwell relations in thermodynamics.)

Added by Alvaro R.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Ryan Griffith

05/25/2022

Step 1

Step 1: Start with the expression for du obtained in Problem 10: du = T ds - p dv Show more…

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Using du in Problem 10, and the text method of obtaining (11.27), show that ((delT)/(delv))_(s)=-((delp)/(dels))_(v). (This is one of the Maxwell relations in thermodynamics.) 10. Given du = T ds - p du, find a Legendre transformation giving (a) a function f(T,v); (b) a function h(s,p); (c) a function g(T,p). Hint for (c): Perform a Legendre transformation on both terms in du. Using du in Problem 10, and the text method of obtaining (11.27), show that OT Op (This is one of the Maxwell relations in thermodynamics.) dv as