first law of Termodynamics

First Law of Thermodynamics

  1. There exists for every system a property called energy, clip_image001. The system energy can be considered as a sum of internal energy, kinetic energy, potential energy, and chemical energy.
    1. Like the Zeroth Law, which defined a useful property, “temperature,” the First Law defines a useful property called “energy.”
    2. The two new terms (compared to what you have seen in physics and dynamics, for example) are the internal energy and the chemical energy. For most situations in this class, we will neglect the chemical energy. We will generally not, however, neglect the internal energy, clip_image002. It arises from the random or disorganized motion of molecules in the system, as shown in Figure 2.1. Since this molecular motion is primarily a function of temperature, the internal energy is sometimes called “thermal energy.”

clip_image003

Figure 2.1: Random motion is the physical basis for internal energy

    1. The internal energy, clip_image002[1], is a function of the state of the system. Thus, or

clip_image005clip_image007, or clip_image009.

Recall that for pure substances the entire state of the system is specified if any two properties are specified. (We will discuss the equations that relate the internal energy to these other variables as the course progresses.)

  1. The change in energy of a system is equal to the difference between the heat added to the system and the work done by the system,

clip_image011

(2..1)

  1. where clip_image001[1]is the energy of the system,
    clip_image013is the heat input to the system, and
    clip_image014is the work done by the system.
    clip_image015(thermal energy) + clip_image017
    1. Like the Zeroth Law, the First Law describes the behavior of the new property
    2. The equation can also be written on a per unit mass basis

clip_image019

 
    1. In many situations the potential energy, kinetic energy, and chemical energy of the system are constant or not important. Then

clip_image020

 
    1. and

clip_image021

 
    1. Note that clip_image022and clip_image014[1]are not functions of state, but clip_image023, which arises from molecular motion (see above), depends only on the state of the system; clip_image023[1]does not depend on how the system got to that state. We therefore have the striking result that:

clip_image025

 
    1. Sometimes this difference is emphasized by writing the First Law in differential form,

clip_image027

(2..2)

    1. where the symbol “clip_image028 ” is used to denote that these are not exact differentials but rather are dependent on path.
    2. Note that the signs are important:
      • clip_image022[1]is defined to be positive if it is transferred to the system; thus the numerical value we substitute for clip_image022[2]will be positive if heat is transferred to the system from the surroundings, and negative if heat is transferred from the system to the surroundings.
      • clip_image014[2]is defined to be positive if it is done by the system (see Section 1.3); thus the numerical value we substitute for clip_image014[3]will be positive if the system is doing work, and negative if work is being done on the system.
    3. For quasi-static processes we can substitute clip_image030,

clip_image032

 
    1. To give an example of where the first law is applied, consider the device shown in Figure 2.2. We heat a gas, it expands against a weight, some force (pressure times area) is applied over a distance, and work is done. The change in energy of the system supplies the connection between the heat added and work done. We will spend most of the course dealing with various applications of the first law — in one form or another.

clip_image033

Figure 2.2: The change in energy of a system relates the heat added to the work done

The form of the first law we have given here is sometimes called the “control mass” form, because it is well suited to dealing with systems of a fixed mass. We will see in Section 2.5 that this form can be written for a control volume with mass flow in and mass flow out (like a jet engine for example). We will call this the “control volume” form of the first law
The first law in closed system

The equation

Ein-Eout=ΔEsystem

clip_image035

Q-W=ΔEsystem=ΔU

Q=ΔU+W

Per unit mass:

q= Δu+w

dq=du+dw

If the process is reversible, then:

dq=du+pdv

This is the first equation of the first law.

Here q, w, Δu is algebraic.

The only way of the heat change to mechanical energy is expansion of working fluid.

The first law in open system

1. Stead flow

For stead flow, the following conditions are fulfilled:

The matter of system is flowing steadily, so that the flow rate across any section of the flow has the same value;

The state of the matter at any point remains constant;

Q, W flow remains constant;

2. Flow work

Wflow=pfΔs=pV

wflow=pv

clip_image037

3.

“ Wt” are expansion work and the change of flow work for open system.

4.

“ Ws” is “ Wt” and the change of kinetic and potential energy of fluid for open system.

5. Enthalpy

for flow fluid energy:

clip_image039

For Per unit mass:

h=u+pv unit: J/kg, kJ/kg

6. Energy equation for steady flow open system

clip_image043

clip_image041

             
  clip_image048
 
    clip_image049
 
    clip_image050
 
    clip_image051

clip_image053Per unit mass:

 
  clip_image055

clip_image057If neglect kinetic energy and potential energy , then:

clip_image059If the process is reversible, then:

This is the second equation of the first law.

7. Energy equation for the open system

clip_image061

Energy equation for the open system

 
  clip_image063

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