List of top Thermodynamics and Statistical Physics Questions

If a thermodynamical system is adiabatically isolated and experiences a change in volume under an externally applied constant pressure, then the thermodynamical potential minimized at equilibrium is the

Consider a three-dimensional system of non-interacting bosons with zero chemical potential. The energy of the system \( \epsilon \propto k^2 \), where \( k \) is the wave vector. The low temperature specific heat of the system at constant volume depends on the temperature as \( C_v = T^{n/2} \). The value of \( n \) is ___ (in integer).

The Hamiltonian of a system of \( N \) particles in volume \( V \) at temperature \( T \) is \( H = \sum_{i=1}^{2N} a_i q_i^2 + \sum_{i=1}^{2N} b_i p_i^2 \) where \( a_i \) and \( b_i \) are positive constants. The ensemble average of the Hamiltonian is \( aNk_B T \), where \( k_B \) is the Boltzmann constant. The value of \( a \) is _____ (in integer).