The molecule as a
whole can move in x, y and z directions with respective components of
velocities and hence possesses kinetic energy.
There can be rotation
of molecule about its center of mass and than the kinetic energy associated
with rotation is called rotational energy.
In addition the bond
length undergoes change and the energy associated with it is called vibrational
energy.
The electron move
around the nucleus and they possess a certain energy that is called electron
energy.
The microscopic modes
of energy are due to the internal structure of the matter and hence sum of all
microscopic modes of energy is called the internal energy.
Bulk
kinetic energy (KE) and potential energy (PE) are considered separately and the
other energy of control mass as a single property (U).
The total energy possessed by the body is
given by:
E = KE + PE + U
Whenever a system interacts with its surroundings, it can exchange
energy in two ways- work and heat.
In mechanics, work is defined as the product
of the force and the displacement in the direction of the force.
Work done when a spring is
compressed or extended: According to Hooke's law
Spring force = - k (x
– x0)
Where k is the spring
constant, x0 is the equilibrium position, and x is the final
position. The negative sign shows that the direction of the spring force is
opposite the direction of the displacement from x0. The external
force is equal in magnitude but opposite in sign to the spring force, so
External force (force
of your hands) = k (x –x0).
Now, we want to calculate
the work done when we stretch the spring from position 1 to position 2.
W = F dx =
k (x – x0) d(x-x0) = 1/2 k [(x2-x0)2
- (x1-x0)2]
Work done when a
volume is increased or decreased
Consider a gas in a container with a movable piston on top. If
the gas expands, the piston moves out and work is done by the system on the
surroundings.
Alternatively, if the gas
inside contracts, the piston moves in and work is done by the surroundings on
the system. Why would the gas inside contract or expand?
It would if the external pressure, Pex, and the
internal pressure, Pin, were different. To calculate the work done
in moving the piston, we know that the force = pressure times area and then
work equals pressure times area times distance or work equals pressure times
the change in volume. So, W = the integral of (Pex) dV
The differential work done (dW)
associated with a differential displacement (dl) is given by
dW =
F dl
For
a piston cylinder assembly,
dW =
F dl = PA (dl) = P dV
If the
gas is allowed to expand reversibly from the initial pressure P to final
pressure P, then the work done is given by
W
= ∫ p dV
The integral
represents the area under the curve on a pressure versus volume diagram.
Therefore the work depends on the path followed and work is a path function and
hence not a property of the system.
The above expression
does not represent work in the case of an irreversible process.
The thermodynamic definition of work is “
Work is said to be done by a system on the surrounding if the sole effect
external to the system could be reduced to the raising of a mass through a
distance”.
Heat like work, is a form of energy.
The
energy transfer between a system and its surroundings is called heat if it
occurs by virtue of the temperature difference across the boundary.
The two modes of energy transfer – work and heat- depend on the choice of the
system.
Heat energy moves from a hotter body to a
colder body upon contact of the two bodies.
If two bodies at different temperatures are
allowed to remain in contact, the system of two bodies will eventually reach a
thermal equilibrium (they will have the same temperature).
A
body never contains heat. Rather heat is a transient phenomenon and can be
identified as it crosses the boundary.