From: hackbard Date: Thu, 19 Jun 2008 17:55:07 +0000 (+0200) Subject: finished last exercise, integral still needs to be done X-Git-Url: https://hackdaworld.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=a1f30138a7ec6b09fd686b31f3555870e82d2ca9;p=lectures%2Flatex.git finished last exercise, integral still needs to be done --- diff --git a/solid_state_physics/tutorial/2_04s.tex b/solid_state_physics/tutorial/2_04s.tex index c115ade..b03977c 100644 --- a/solid_state_physics/tutorial/2_04s.tex +++ b/solid_state_physics/tutorial/2_04s.tex @@ -215,14 +215,21 @@ {\left.\frac{\partial p}{\partial V}\right|_T}=0 \] \item $\frac{1}{B}=-\frac{1}{V}\left.\frac{\partial V}{\partial p}\right|_T$ - and $\alpha_V=\frac{1}{V}\left.\frac{\partial V}{\partial T}\right|_p$ + and $\alpha_V=\frac{1}{V}\left.\frac{\partial V}{\partial T}\right|_p$\\ \[ - C_p-C_V=\left.\frac{\partial E}{\partial T}\right|_p- - \left.\frac{\partial E}{\partial T}\right|_V= - \frac{\partial E}{\partial S} - \left.\frac{\partial S}{\partial T}\right|_p- - \frac{\partial E}{\partial S} - \left.\frac{\partial S}{\partial T}\right|_V= + C_p=\left.\frac{\partial H}{\partial T}\right|_p= + \left.\frac{\partial H}{\partial S}\right|_p + \left.\frac{\partial S}{\partial T}\right|_p= + T\left.\frac{\partial S}{\partial T}\right|_p + \] + \[ + C_V=\left.\frac{\partial E}{\partial T}\right|_V= + \left.\frac{\partial E}{\partial S}\right|_V + \left.\frac{\partial S}{\partial T}\right|_V= + T\left.\frac{\partial S}{\partial T}\right|_V + \] + \[ + \Rightarrow C_p-C_V= T\left.\frac{\partial S}{\partial T}\right|_p- T\left.\frac{\partial S}{\partial T}\right|_V= T\left( @@ -238,17 +245,21 @@ \left.\frac{\partial S}{\partial T}\right|_V= \left.\frac{\partial S}{\partial T}\right|_p+ \left.\frac{\partial S}{\partial p}\right|_T - \left.\frac{\partial p}{\partial T}\right|_V, + \left.\frac{\partial p}{\partial T}\right|_V \] - the Maxwell relation + and the Maxwell relation \[ \left.\frac{\partial S}{\partial p}\right|_T= -\left.\frac{\partial V}{\partial T}\right|_p \] - and (for a process with constant volume) + and the equality \[ - 0=dV=\left.\frac{\partial V}{\partial T}\right|_p dT+ + dV=\left.\frac{\partial V}{\partial T}\right|_p dT+ \left.\frac{\partial V}{\partial p}\right|_T dp + \stackrel{\left.\frac{\partial}{\partial T}\right|_V}{\Rightarrow} + 0=\left.\frac{\partial V}{\partial T}\right|_p+ + \left.\frac{\partial V}{\partial p}\right|_T + \left.\frac{\partial p}{\partial T}\right|_V \Rightarrow \left.\frac{\partial p}{\partial T}\right|_V= -\frac{\left.\frac{\partial V}{\partial T}\right|_p}