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 one year ago
Derive an expression for the contribution to the molar heat capacity at constant volume CV,m(T) of Cl atoms from these electronic states and evaluate it for T = 500 K.
 one year ago
Derive an expression for the contribution to the molar heat capacity at constant volume CV,m(T) of Cl atoms from these electronic states and evaluate it for T = 500 K.

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Frostbite
 one year ago
Best ResponseYou've already chosen the best response.0Theory: The electronic ground state of the Cl atom is fourfold degenerate, while the first electronically excited state is doubly degenerate and lies 881 cm–1 above the ground state.

Frostbite
 one year ago
Best ResponseYou've already chosen the best response.0Work so far; \[C _{V,m}=\left( \frac{ \partial U _{m} }{ \partial T } \right)_{V}=\frac{ N _{a} \left( \langle \epsilon ^{2} \rangle  \langle \epsilon \rangle ^{2} \right) }{ kT ^{2} }\] \[\langle \epsilon \rangle=\sum_{i}^{n}p _{i} \epsilon _{i}\] \[\langle \epsilon \rangle=\frac{ 4 }{ q } \epsilon _{0}+\frac{ 2e ^{ \beta \epsilon} }{ q } \epsilon=\frac{ 2e ^{ \beta \epsilon} }{ q } \epsilon\] \[\langle \epsilon ^{2} \rangle=\sum_{i=0}^{1} p _{i} \epsilon ^{2} _{i}=\frac{ 4 }{ q } \epsilon _{0} ^{2}+\frac{ 2e ^{ \beta \epsilon} }{ q } \epsilon ^{2}=\frac{ 2e ^{ \beta \epsilon} }{ q } \epsilon ^{2}\\\] \[C _{V,m}=\frac{ N _{A}\left( \frac{ 2e ^{ \beta \epsilon} }{ q } \epsilon ^{2}\left( \frac{ 2e ^{ \beta \epsilon} }{ q } \epsilon \right)^{2} \right) }{ kT ^{2} }\] Now from here things are going down hill. I know I need to substitute the equation: \[E=\frac{ hc }{ \lambda } \Leftrightarrow \epsilon=hc \bar{v}\] But at the same time I like to make the expression more simple.

Frostbite
 one year ago
Best ResponseYou've already chosen the best response.0@ataly @aaronq @blues @Preetha @amistre64

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0if your notation is correct, i dont see way that e^2 cant be factored out of the top

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0other than that, i got no idea what the setup is doing :)

Frostbite
 one year ago
Best ResponseYou've already chosen the best response.0I don't follow the exponential function to 2?

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0its all a bit above my reading abilities :/ srry

Frostbite
 one year ago
Best ResponseYou've already chosen the best response.0p = Boltzmann distribution q = the molecular partition function. beta = the thermodynamical beta (dah?) CV,m = molar heat capacity epsilon = the energy.

Frostbite
 one year ago
Best ResponseYou've already chosen the best response.0The method for solving the problem I wrote up for my self was the following: 1. The heat capacity at constant volume is related to the variance of the molecular energy levels. 2. Calculate the mean value of the electronic energy of Cl atoms <epsilon> and the mean value of the square of the electronic energy of Cl atoms <epsilon^2>. 3. insert the results from step 2. into the expression from step 1.
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