Thermodynamics/Energy

Note: This section needs a very basic knowledge of calculus. To see a simplified version go HERE

Work

 * Work : Force acting through a distance

Therefore, Work, W is

$$dW=-Fdl$$

where F is force and dl is the distance through which the force acts The reason for the minus sign is explained below. In most applications of thermodynamics we are mainly interested in mechanical work due to pressure of a fluid. Since pressure is force per unit area, force is simply pressure times area:

$$F=-PA$$

If we consider a volume, V, then the distance l is

$$l=\frac{V}{A}$$

or

$$dl=d(\frac{V}{A})$$

Then,

$$dW=-PAd(\frac{V}{A})$$

If we then assume a constant area then we can take the A inside the differential and:

$$\color{OliveGreen}dW=-PdV$$

Integrating gives

$$W=-\int_{V_1}^{V_2}PdV$$

Energy

 * Energy : Capacity to do work


 * Internal Energy, U : The total energy of the system

Heat

 * Heat : Energy transferred due to a temperature difference


 * Adiabatic : No heat transfer between a system and its surroundings


 * Exothermic process : A process which releases heat


 * Endothermic process : A process which adsorbs heat

Heat is denoted by the symbol, Q

Heat and work are not properties
It is important to note that heat and work are not intrinsic properties of a system. They refer only to energy which is transferred. We cannot say, for example, that a brick has 15 J of heat. It may however, have 15 J of energy.

Sign convention and notation
Heat and work are considered positive if they are transferred from the surroundings to the system. This is the reason for the negative sign in the work equations above.

&Delta; is used to indicate finite change (for example, &Delta;U )

d is used to indicate differential change (for example, dU )

However, we do not use &Delta;Q or &Delta;W for finite changes in heat or work, since Q and W only refer to change. We but simply use just Q or W. We still do use dQ and dW for differential change.

Observations
The laws of thermodynamics are based on observations of the natural world. The first law is based on two observations concerning energy:


 * Energy can be transferred between a system and its surroundings by only two ways: work and heat
 * The total energy of a system and its surroundings is always constant (The conservation of energy)

First Law
These two observations can be combined into the First Law of Thermodynamics :

The internal energy of a system is constant unless changed by doing work or by heating

Mathematical Statement
Mathematically, the change in internal energy is the sum of the work and heat entering or leaving the system: $$\Delta U = Q + W$$

or

$$dU = dQ + dW$$