chiaki
Mar30-10, 01:22 AM
1. The problem statement, all variables and given/known data
In deriving <E2>-<E>2
starting from <E>=U=sum(Eiexp(-beta Ei))/sum(exp(-beta Ei). the taking derivative of U with respect to beta, the book always notes E (thus Volume) is held constant. what i am trying to do is taking the derivative of U with respect to beta or T (temp) and V (volume). but i get stuck
2. Relevant equations
<E>=U= sum(Ei*exp(-beta*Ei)/sum(exp(-beta*Ei)
dU=dU/dT+dU/dV
3. The attempt at a solution
I applied the above equation dU to U as listed above. i performed the quotient and product rule obtaining terms partial derivative with respect to V and T. I tried to look for a way to combine terms and cancel terms. but I cannot. anyone help thank you.
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
In deriving <E2>-<E>2
starting from <E>=U=sum(Eiexp(-beta Ei))/sum(exp(-beta Ei). the taking derivative of U with respect to beta, the book always notes E (thus Volume) is held constant. what i am trying to do is taking the derivative of U with respect to beta or T (temp) and V (volume). but i get stuck
2. Relevant equations
<E>=U= sum(Ei*exp(-beta*Ei)/sum(exp(-beta*Ei)
dU=dU/dT+dU/dV
3. The attempt at a solution
I applied the above equation dU to U as listed above. i performed the quotient and product rule obtaining terms partial derivative with respect to V and T. I tried to look for a way to combine terms and cancel terms. but I cannot. anyone help thank you.
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution