Thermodynamics Lecture 2:
1st law of thermodynamics
the kinetic gas theory has shown that heat is nothing but a form of energy, this implies that there are many different forms of energy
the quantity of energy in a fully closed system remains constant, ( the internal energy of a isolated system is constant
Work
Motion against an opposing force, work is done when a force moves
Work is a transfer of energy that utilizes or causes uniform motion of atoms in the surroundings
A force (F) moving a distance (X) does equal work to Fx. the most common form of work (and often the only one we have to consider) is the work done against the surrounding pressure as the volume V increases
However many chemical changes also do work by releasing electrical energy or light
With work (W) being a primary concept in thermodynamics, we need to donate the capacity of a system to do work
ENERGY: a measure of the capacity of a system to do work
HEAT: is the description of a process, it is the means by which energy is transferred from a hotter body to a cooler one in order to equalize their temperatures
INTERNAL ENERGY (U)
the internal energy is the kinetic energy due to the motion of molecules and potential energy(associated with the atoms within molecules or crystals )
The internal energy depends on, translational kinetic energy, molecular rotation, bond vibration, intermolecular attractions, chemical bonds, electrons
State and Path functions
The internal energy (U) ,(enthalpy and entropy ) are state functions
Heat (q) and work (W) are path functions
a STATE FUNCTION is one whose value only depends on the state of the substance under consideration, it ha the same value for a given state no matter how that state came about
In contrast a PATH FUNCTION depends on the path which the system takes in going between two states
state functions are exact differentials
Sign Conventions
Both heat and work are signed quantities
+q heat is absorbed by the system (an endothermic process)
-q heat is given out by the system (an exothermic process)
for work(W), the work done on the system. it therefore follows that when a gas is compressed by an external force the work is positive, whereas when the gas expands by pushing against an external force the work is negative
GAS EXPANSION
we imagine an ideal piston(one with no mass that moves without friction) with an area A which contains a gas at a pressure p internal and where the external pressure is p external
Under conditions where p int > p ext, the piston will move out (by a distance of dx ) and in doing so does work dw' ( =-dw) against the external pressure
the work done by the gas (system) is therefore dw' = force x distance = p ext area dx = p ex dVolume
the work done on the gas dw is simply, dw = -dw' = -p ext dV
if p ext = 0, (in vacuum) then clearly no work is done
If p ext is constant then we can calculate the work done by the piston when it expands from its initial volume Vi to its final volume Vf
ENERGY cannot be created or destroyed but is just transformed from one form to another
We have already seen that the forms of energy are heat (q), work (W) and internal energy(U)
The first law can be expressed mathematically in the following way : if we take a system from state A to state B, then there is a definite change in the internal energy : DELTA U = Ub - Ua
Where Ua and Ub are the internal energies of the system in two states, this energy change can appear as heat / and or work provided that their sum, q + w = DELTA U
Therefore the first law can also be expressed in the way
DELTA U = q + w
If we look at infiniteismally small changes (reversible ) in U and infiniteismally small amounts in q and w
dU = dq + dw
if we now simplify so that only PV work is done on the system
dU = dq - d(pV)
A change where the surroundings are a perfect vacuum (p= 0)
A change at constant volume (isochoric ) (dV = 0 )
A change where the surroundings are at constant pressure (dp=0)
DELTA U = q + w, dw = -dw' = - p exterior dV, dU = dq, no work is done as p = 0
(dV = 0), dU = dq, exothermic reaction = -q DELTA U is negative internal energy is decreased, endothermic reaction + q, DELTA U is positive, internal energy increases
helps us to predict under what conditions maximum work is done, the external pressure should be as high as possible so as to maximize the work,
however if the external pressure exceeds the internal pressure than the gas is compressed,
therefore to obtain the maximum expansion work the external pressure needs to be a LOT smaller than the internal pressure