elduderino
Sep29-10, 06:02 PM
1. The problem statement, all variables and given/known data
Consider a system of N noninteracting particles in a container of cross-sectional area A. Bottom of the container is rigid. The top consists of an airtight, frictionless piston of mass M. Neglect the potential energy of the molecules of gas.
Construct the partition function Q of the (N+1) particle system (N particles of mass m+ piston)
Calculate the fluctuations in the volume of the system?
2. Relevant equations
Z= \frac{1}{N!h^{3N}}\int e^{-\beta H(p,q)}d^3pd^3q
3. The attempt at a solution
System is in equilibrium for theory to be applicable, hence piston is at rest at some height y.
H(p,q) = \sum_i \frac{p_i^2}{2m} +mgy
6N+1 dimensional phase space
Z= \frac{1}{N!h^{3N}}\int e^{-\beta (\sum_i \frac{p_i^2}{2m} +mgy )}d^3pd^3q dy
Consider a system of N noninteracting particles in a container of cross-sectional area A. Bottom of the container is rigid. The top consists of an airtight, frictionless piston of mass M. Neglect the potential energy of the molecules of gas.
Construct the partition function Q of the (N+1) particle system (N particles of mass m+ piston)
Calculate the fluctuations in the volume of the system?
2. Relevant equations
Z= \frac{1}{N!h^{3N}}\int e^{-\beta H(p,q)}d^3pd^3q
3. The attempt at a solution
System is in equilibrium for theory to be applicable, hence piston is at rest at some height y.
H(p,q) = \sum_i \frac{p_i^2}{2m} +mgy
6N+1 dimensional phase space
Z= \frac{1}{N!h^{3N}}\int e^{-\beta (\sum_i \frac{p_i^2}{2m} +mgy )}d^3pd^3q dy