In this article we will discuss about:- 1. Introduction to First Law of Thermodynamics 2. First Law for a Closed System Undergoing a Process 3. Energy — A Property of the System 4. Different Forms of Stored Energies 5. Specific Heat at Constant Pressure and Specific Heat at Constant Volume 6. Adiabatic Index 7. Perpetual Motion Machine of First Kind [PMM – 1] and Few Other Details.
Contents:
- Introduction to First Law of Thermodynamics
- First Law for a Closed System Undergoing a Process
- Energy — A Property of the System
- Different Forms of Stored Energies
- Specific Heat at Constant Pressure and Specific Heat at Constant Volume 6.
- Adiabatic Index
- Perpetual Motion Machine of First Kind [PMM – 1]
- Flow Process; Control Volume; Control Surface
- Flow Work or Flow Energy
- Conditions of Steady Flow System
- Steady Flow Energy Equation (S.F.E.E.)
- Limitations of First Law of Thermodynamics
1. Introduction to First Law of Thermodynamics:
Energy is inherent in all matters. Energy may appear in many different forms. Conversion can be made from one form of energy to another. We are unable to define the general term energy in a simple way, but we can define with precision the various forms in which it appears.
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One of the consequences of Einstein’s theory of Relativity is that mass may be converted into energy and energy into mass, the relation being given by the famous equation,
Energy (E) = m (mass) x C2 (where C – velocity of light)
Energy is a scalar quantity, not a vector quantity.
Except the nuclear reaction, (where mass is converted into energy) total energy of the universe is constant. For this matter, First Law of Thermodynamics can be expressed as—
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Energy can neither be created nor destroyed (except in nuclear reactions). This is the law of conservation of energy.
2. First Law for a Closed System Undergoing a Process
:
If a closed system undergoes a change of state or a process and during which, both work transfer and heat transfer are involved, then the net energy transfer will be stored within the system. If Q is the amount of heat transferred to the system and W is the amount of work transferred from the system, during the process, and then the net energy transfer (Q — W) will be stored in the system.
Energy in storage is neither heat nor work, but is called as Internal energy or simply energy of the system.
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∴ Q – W = ΔE
or Q = ΔE + W
Where ΔE is the change in energy. Here Q, W and ΔE all are expressed in joules.
3. Energy — A Property of the System:
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Consider a system which changes its state from state (1) to state (2) by following the path A, and returns from state (2) to state (1) by following the path B as shown in Fig. 2.4. So the system undergoes a cycle. Now writing the I-law for the path A,
Thus the change in energy for the path B and C are same. Hence change in energy does not depend upon path, so it depends on end states. Hence, it is a point function and since properties are point functions, Energy is a property of the system.
4. Different Forms of Stored Energies
:
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The total energy E is made up of Kinetic Energy (K.E.), Potential Energy (P.E.) and Internal Energy (I.E.).
∴ E = K.E. + P.E. + I.E.
Kinetic Energy is due to the motion of the fluid in the system. Potential Energy is the energy due to the gravitational force.
A part of the total energy which is stored in the molecular and atomic structure is known as Internal energy and is denoted by U.
In the absence of Kinetic Energy and Potential Energy i.e., when
Internal Energy (U):
It is the energy stored in the molecular structure due to heat and work interactions.
or
In case of gases we know that the gas is made up of a number of molecules, which are moving continuously. I.E. is the energy which arises from the motion of these molecules.
If the temperature of the gas is increased, the molecular activity increases, therefore the I.E. also increases. Thus I.E. is a function of temperature and its value can be increased or decreased by adding or removing heat to or from the system.
Due to practical difficulties it is very difficult to determine the absolute value of Internal energy. Fortunately, in most of the thermodynamic applications change in I.E. is used, since changes in the states of a system are considered. Change in I.E. is denoted by ΔU and ΔU = U2 – U1.
For unit mass,
Enthalpy (H):
It is an extensive property, since its value depends on mass. Enthalpy of a substance is given by the sum of Internal energy and Pressure-Volume product.
i.e., H = U + PV and specific enthalpy, h = u + Pv
5. Specific Heat at Constant Pressure and Specific Heat at Constant Volume
:
Specific heat of a gas is defined as the amount of heat required to rise the temperature of unit mass of a gas through one degree.
There are 2-types of specific heats:
1. Specific Heat at Constant Volume Cv :
It is the amount of heat required to rise the temperature of unit mass of a gas through one degree when the volume is constant.
If a unit mass of a gas is taken in a closed vessel and is heated, the volume of the gas remains constant, but the temperature increases. As the volume remains constant, there is no external work done by the gas and as temperature of the gas increases, there is increase in internal energy of the gas.
Therefore heat supplied to the gas is completely utilized in increasing the I.E. of the gas,
2. Specific Heat at Constant Pressure Cp:
It is the amount of heat required to rise the temperature of unit mass of a gas through one degree when the pressure is kept constant.
Consider a unit mass of a gas in a cylinder fitted with a frictionless piston. When the gas is heated, the piston moves up, maintaining the same pressure. But the volume and temperature of the gas increases during heating.
As there is increase in volume, there is external work done by the gas and there is increase in temperature, there is increase in I.E.
Thus heat supplied when the pressure is constant, is utilized for two purposes:
(a) To do some external work.
(b) To increase the I.E of the gas.
Whereas in case of constant volume heating, the heat supplied is completely utilized for increasing the I.E.
∴ Specific heat at constant pressure is greater than specific heat at constant volume.
Therefore, Cp is also defined as, the rate of change of specific enthalpy with respect to temperature when the pressure is kept constant.
6. Adiabatic Index
:
It is the ratio of specific heat at constant pressure to the specific heat at constant volume and is given by,
7. Perpetual Motion Machine of First Kind [PMM – 1]:
First law states the general principle of conservation of energy i.e., energy can neither be created nor be destroyed but it can be transformed from one form to the other.
But PMM-1 is defined as a machine which will produce continuous work output without receiving any energy from any other system or the surroundings.
It will create energy and thus violates I-Law of thermodynamics. All the attempts made so far to make such a machine have failed, thus they show the validity of I-law. Thus PMM-1 is just a conceptual machine.
Converse of PMM-1 is also true i.e., there can be no machine which would continuously consume work, without producing some other form of energy.
8. Flow Process; Control Volume; Control Surface
:
Flow Process:
Processes performed in the open systems are called as Flow-processes.
Figure 2.9 shows a portion of steam power plant. High pressure steam enters the steam turbines at Section (I), expands and produces work output and then it leaves the turbine at section (2). For analysing the expansion process, 2-methods are used.
In the first method certain mass of the fluid Marked A is considered and this is supposed to flow through the turbine.
In the second method, certain fixed volume of the system known as Control Volume (CV) is considered. The moving substance flows through this control volume. The surface of the control volume is known as Control Surface (CS).
9. Flow Work or Flow Energy
:
In case of flow processes certain amount of work or energy is required to push the fluid into and out of the system. This work energy is known as flow work or flow energy. Consider a flow process as shown in Fig. 2.10.
Let F, be the force which forces the mass m1, of cross sectional area A1 into the system against the pressure P1 of the system. Now consider a small amount of work done on the system in causing the displacement dl1 for the mass m1.
Thus the small amount of work done on the system in causing the displacement dl1,
Note: Since the flow work is entirely expressed in terms of properties of the system, the net flow work depends on the end states and it is a Property. Whereas the other forms of work are path functions so in problems involving flow processes, flow work is to be calculated separately.
10. Conditions of Steady Flow System
:
A steady flow process should satisfy the following conditions:
(i) The mass flow rate into and out of the system are equal and do not vary with time i.e., mass in the system does not change.
(If the mass flow rate at the inlet is 10 kg/sec., then the mass flow rate at the exit will be 10 kg/sec and it does not vary with time i.e., if we note the mass flow rate say, when we come to the college and while going home also it will be same.)
(ii) The energy of the fluid at the entrance and at the exit are same and do not vary with time.
(iii) The rates of heat and work transfer into and out of the system do not vary with time.
11. Steady Flow Energy Equation (S.F.E.E.)
:
Steady flow energy equation is obtained by applying the first law of thermodynamics to a steady flow system.
Steady Flow Energy Equation on Mass Basis:
For deriving this, we have to consider m = 1 kg/sec and all other quantities will be for per kg mass such as δW/dm and δQ/dm.
∴ Equation (1) becomes,
This is the SFEE on mass basis.
In a Steady Flow System W.D.= -∫ v.dp when Changes in KE and PE are Neglected:
We know that, SFEE on mass basis. From Eq. (3)
Significance of ∫Pdv in Case of Steady Flow Process and Non-Flow Process:
Continuity Equation or Law of Conservation of Mass:
Continuity Equation is based on the Principle of Conservation of Mass:
12. Limitations of First Law of Thermodynamics
:
The first law of thermodynamics is simply a law of conservation of energy and has its own limitations.
These limitations are:
1. The law considers all forms of energies equivalent i.e., the first law of thermodynamics is a law of energy equivalence. This law is necessary condition so far as the account of energy balance is concerned with the possibility of transformation of one kind of energy to another.
2. The first law does not consider the direction of energy transformation.
3. The first law of thermodynamics does not consider the grade of the energy or energy reservoirs. It, assumes that all energy reservoirs are identical.
The second law of thermodynamics relates to the direction of energy exchange processes. One of the statements of the second law of thermodynamics is Clausius statement and states that no cyclic process is possible whose result is the flow of heat out of a heat reservoir at one temperature and the flow of an equal quantity of heat into a second reservoir at a higher temperature, without external work.
Or, heat cannot flow from one body at a lower temperature to the another body at higher temperature without any external work.
This principle is used in a refrigerator. For refrigerator external power is supplied to the compressor.
The third law states that the entropy of a pure substance is zero at absolute zero temperature.