We study the simplest possible model of nanocrystal consisting in a simple cubic lattice with a small number of atoms (NA ∼ 10 - 103) where each atom is linked to its nearest neighbor by a quantum harmonic potential. Some properties (entropy, temperature, specific heat) of the nanocrystal are calculated numerically but exactly within the framework of the microcanonical ensemble. We find that the presence of a surface in the nanocrystal modifies the thermostatistic properties to a greater extent than the small number of atoms in the system. The specific heat Cυ behaves similarly to the Einstein solid, with an asymptotic value for high temperatures that differs from that of the Dulong-Petit law by a term of the order of N A - 1 / 3 and that can be explained easily in terms of the surface. The entropy is non-additive, but this is due to the presence of the surface and we show that the additivity is recovered in the thermodynamic limit. Finally, we find that, when calculations follow the canonical ensemble, results differ little for small systems (NA = 27) and are inexistent for larger systems NA = 100).

The work done by a parallel plate capacitor is evaluated when the plate separation is changed. Two cases are considered: 1) when the capacitor has a constant charge; 2) when the capacitor is at constant voltage. The net work is calculated when the device follows a closed cycle in the charge-voltage space. For certain conditions a net mechanical work can be obtained from the cycling capacitor. The analysis is simple enough to be explained in a general physics course.

Se ha evaluado el trabajo realizado por un capacitor plano cuando se cambia la separación entre las placas. Se consideran dos casos: 1) el capacitor tiene carga constante; 2) el capacitor está a potencial constante. Se calcula el trabajo neto cuando el dispositivo realiza un ciclo cerrado en el espacio de carga-voltaje. Bajo ciertas condiciones, se puede obtener trabajo mecánico neto del capacitor. El análisis es lo suficientemente simple como para ser explicado en un curso de física general.

O movimento de um projétil com velocidade horizontal inicial V0, movendo-se sob ação do campo gravitacional e de uma força de arrasto é estudado analiticamente. Como sabemos, o projétil alcança uma velocidade terminal Vterm. Existe um resultado curioso sobre a velocidade mínima Vmin; acontece que a velocidade mínima é menor que a velocidade terminal se V0 > Vterm e é menor do que a velocidade inicial se V0 < Vterm. Estes resultados mostram que a velocidade não é uma função monotônica.

The motion of a projectile with horizontal initial velocity V0, moving under the action of the gravitational field and a drag force is studied analytically. As it is well known, the projectile reaches a terminal velocity Vterm. There is a curious result concerning the minimum speed Vmin; it turns out that the minimum velocity is lower than the terminal one if V0 > Vterm and is lower than the initial one if V0 < Vterm. These results show that the velocity is not a monotonous function. If the initial speed is not horizontal, there is an angle range where the velocity shows the same behavior mentioned previously. Out of that range, the velocity is a monotonous function. These results comes out from numerical simulations.