A system consists of a battery in a fixed–volume container. the battery has a very large but finite internal electrical resistance and, as a result, slowly but spontaneously discharges with time. Assume that the battery has only two independent properties: energy E and charge C. Typically, the charge is measured in ampere–hours. From the descriptions below, indicate the type of state of the system. Explain your answers.
(a) the container walls are impermeable to energy. the battery is charged and its electrodes are not connected to any external device. Consider both short and long periods of time.
(b) Same as in part (a), except that the battery is now fully discharged.
(c) Same as in part (a), except that the electrodes are now connected to a battery charger that maintains the charge at a constant value.
(d) Same as in part (c), except that the battery also interacts with a system that maintains the battery energy at a constant value.
