An Ensemble provides the physical description of the system.
A system can be completely described interms of the three components of the velocity and position each for every atom in the system. But, this is an almost impossible information to collect.
Instead, while describing a system, people use measurable average properties like energy, pressure etc. These properties do not depend on the individual characterization of each constituting atom of the system.
But, at the same time these properties also do not characterize the system completely.
One set of values of these properties may correspond to different states of the system. Based only on one set of properties thus, it is thus difficult to pinpoint at a particular state of the system. So every possible state of a system has equal probability corresponding to a value of measurable average property .
At a given time, the system can be in only one state. If the same system with one set of properties is considered exisiting at different time steps are considered, it is found to exist in different states.Each such different state of a system which can be characterized by the same set of measurable average properties are called ensemble. Statistical mechanics deals with ensemble instead of individual systems.
Depending on the properties used to define a system there are different ensembles:
Microcanonical ensemble (NVE) : The ensemble characterized by a fixed number of atoms, N, a fixed volume, V, and a fixed energy, E. Thus it is isolated from changes in moles (N), volume (V) and energy
(E). Since the total energy for the system remains constant, no energy is lost in the form heat exchange, that makes the the system adiabatic in nature.
Canonical Ensemble (NVT): The ensemble is characterized by a fixed number of atoms, N, a fixed volume, V, and a fixed temperature, T. Since the temperature in this ensemble remains constant, the energy needs to be exchanged with the surrounding which can be done with the medium of thermostat.
Isobaric-Isothermal Ensemble (NPT): This ensemble is characterized by a fixed number of atoms, N, a fixed pressure, P, and a fixed temperature, T. In addition to a
thermostat, a barostat is needed.
Grand canonical Ensemble (mVT): The thermodynamic state for this ensemble is characterized by a fixed chemical potential, m, a fixed volume, V, and a fixed temperature, T.
A system can be completely described interms of the three components of the velocity and position each for every atom in the system. But, this is an almost impossible information to collect.
Instead, while describing a system, people use measurable average properties like energy, pressure etc. These properties do not depend on the individual characterization of each constituting atom of the system.
But, at the same time these properties also do not characterize the system completely.
One set of values of these properties may correspond to different states of the system. Based only on one set of properties thus, it is thus difficult to pinpoint at a particular state of the system. So every possible state of a system has equal probability corresponding to a value of measurable average property .
At a given time, the system can be in only one state. If the same system with one set of properties is considered exisiting at different time steps are considered, it is found to exist in different states.Each such different state of a system which can be characterized by the same set of measurable average properties are called ensemble. Statistical mechanics deals with ensemble instead of individual systems.
Depending on the properties used to define a system there are different ensembles:
Microcanonical ensemble (NVE) : The ensemble characterized by a fixed number of atoms, N, a fixed volume, V, and a fixed energy, E. Thus it is isolated from changes in moles (N), volume (V) and energy
(E). Since the total energy for the system remains constant, no energy is lost in the form heat exchange, that makes the the system adiabatic in nature.
Canonical Ensemble (NVT): The ensemble is characterized by a fixed number of atoms, N, a fixed volume, V, and a fixed temperature, T. Since the temperature in this ensemble remains constant, the energy needs to be exchanged with the surrounding which can be done with the medium of thermostat.
Isobaric-Isothermal Ensemble (NPT): This ensemble is characterized by a fixed number of atoms, N, a fixed pressure, P, and a fixed temperature, T. In addition to a
thermostat, a barostat is needed.
Grand canonical Ensemble (mVT): The thermodynamic state for this ensemble is characterized by a fixed chemical potential, m, a fixed volume, V, and a fixed temperature, T.
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