Contents of the Applied Thermodynamics :

 Introduction to Thermodynamic Systems.  

 Units and Dimensions.

 Work Transfer.

Temperature and Heat.

The First Law of Thermodynamics.

Flow Processes.

The Second Law of Thermodynamics and Air Standard Cycles.

Properties of Pure Substances.

Thermodynamic statements , Definitions and Formulae.

Thermodynamics Statements , Definitions and Formulae

A thermodynamic system is a collection of matter that is enclosed by a closed boundary(system boundary).

A closed system is one in which matter does not cross the system boundary.

An open system is one in which matter crosses the system boundary.

Systems can have two types of boundary interactions. These are activities that allow work or heat to cross the system boundary.

A heat interaction happens due to a temperature difference across the boundary.

A work interaction  can be due to the action of a force or a torque , addition of electrical charge , magnetization etc. In theory , any kind of work interaction could be fully converted into another kind of work interaction by using a suitable device such as a motor (electrical work to rotational mechanical work) , a pulley attached to a rotating shaft (rotational mechanical work to work by linear displacement of a force) or any such arrangement.

The state of a system refers to the overall condition of a system. If the state of a system is known , all the physical properties of the system are known.

For a pure substance , it is enough to know two suitable properties to determine its thermodynamic state. This rule is known as the two-property rule.

In thermodynamics , all pure chemical substances are pure substances. Uniform mixtures of fluids , liquid solutions and alloys can also be treated as pure substances.

Intensive and extensive properties of a system :

Any property of a system that can be defined at a point within the system is an intensive property.          A property that can be defined only for a whole system is an extensive property.

Temperature(T) , pressure(p) and specific volume(v) , viscocity(µ) , are examples of intensive properties.

Mass(m,M) , and volume of a system are extensive properties. 

A simple thermodynamic system(simple system) is one in which only the energy stored in the form of internal energy (heat energy or sometimes heat energy + chemical energy) is important.

This is because the change in energy contained in other forms like kinetic , potential , electrical and elastic energy is negligible.

A process is an activity that causes the state of a system to change. 

Process usually involve work and/or heat interactions and sometimes no interaction.

To be able to determine theoretically the heat and work interaction during a process , the state of a system should be known during the whole process. This is made possible in some thermodynamic processes by assuming the process to be quasi-static(almost static and in equilibrium for all practical purposes). A quasi-static expansion (or compression of a fluid) is also a fully resisted process.  

A cyclic process( cycle , thermodynamic cycle) is one in which a system is returned to its initial state at the end of the process. A cyclic process may consist of a sequence of processes.

Two systems are in thermal equilibrium if no heat will flow between them when they are brought into contact. The zeroth law of Thermodynamics states that if each of two systems can be separately at thermal equilibrium with a third , then they can be at equilibrium with each other.

From this law we learn that systems in equilibrium have a property in common and we identify this property as temperature.

Heat interaction across a system boundary take place only when there is a temperature difference across the system boundary.

The First law of Thermodynamics can be stated in several ways. The following applies to a closed system :

If a system is taken through a cyclic process the algebraic sum of the heat received by the system and the work done on the system is zero.

So , is not possible to have a device that will continue to produce work without receiving any form of energy.(Such a device is called a perpetual motion machine of first kind or PMM1)   

The First law leads to another important result that the internal energy , U of a system is a property of the system and therefore its value depends only on the state of the system.
For a closed system ;

ΔU = Q +W

Where ΔU is the change in internal energy of the system and Q and W are , respectively , the heat supplied to it and the work done on it.

For a process that takes the system from state 1 to state 2 the equation becomes ;

U₂ – U₁ = Q_1-2 + W_1-2 

In a cyclic process , the state at the end of the process is the same as that at the start. thus we have ;

φ dQ + φ dW = 0  

Or simply ;                                                      Q + W = 0

where Q and W are the heat and work going into the system during the cycle.

In an open system , equations are written for the conservation of matter and conservation of energy( A modified version of the first law equation for closed system).

M_f –M_i = ∑ m_j         ( equation of continuity)

Where M is mass inside the system. subscripts i and f refer to the start and end of the period of flow considered. subscript j refers to the stream through which flow occurs. 

E_f - E_i = Q + W + ∑m_j (h_j - c_j²/2 + gz_j)

(unsteady flow energy equation , UFEE) When the energy (E) inside the system is only internal energy(U) , the equation is written as , 

 U_f - U_i = Q + W + ∑m_j (h_j - c_j²/2 + gz_j)

Where m , h , c , g and z refer to the mass crossing the system boundary at a given location , the specific enthalpy , velocity , acceleration due to gravity and elevation above a reference level.


Enthalpy (H = U + pV) is the sum of internal energy and 'flow work' (pV) , the work to transfer the fluid across the system boundary. specific enthalpy (h =pv) is enthalpy per unit mass.


When a flow is steady ,  U_f  =  U_i  and the UFEE changes to ;
Q + W + ∑m_j (h_j + c_j²/2 + gz_j) = 0    (steady flow energy equation , SFEE)
The continuity equation , the UFEE and SFEE becomes fewer. For a single stream through which mass m enters an open system ;

M_f - M_i = m

U_f - U_i = Q + W + m (h + c²/2 + gz) 

The equations are used in problems of charging and discharging of pressure vessels.

For steady flow arrangement with two streams (one inlet and one outlet) , if matter entering the leaving is m , the SFEE is ;

m { (h₂ – h₁) + (c₂² – c₁²) / 2 + g (z₂ – z₁) } + Q + W = 0

Work

In mechanics , work is defined in mechanics as the scalar product of force and displacement of its point of application.

Thermodynamics recognizes other forms of work too. Work is defined as any boundary interaction whose entire effect could be converted fully into that of a force undergoing displacement. 

Boundary expansion work is important in thermodynamics : If the volume V of closed system S at pressure p increases by dV , the boundary expansion work done on the system is ;

dW = -p dV

For a process taking a system from state 1 to state 2 ;

W_1-2 = - ₁∫² p dV

For a quasi-static process taking a system from state 1 to state 2 , and following the law                 pVⁿ = constant ;

W_1-2 = (p₂V₂ – p₁V₁) / (n-1)

(take care about the case of n=1).

If the relationship between p and V is in the form of a table or graph a suitable numerical or graphical method may be used.

For a cyclic process ;

 φ dQ + φ dW = 0

Working fluids:

For a perfect gas , the equation of state is ;

 pV = mRT

For a quasi-static process following the law ;

pVⁿ = constant

the work done during process 1-2 is ;

W_1-2 = mR(T₂ – T₁) / (n-1)

And ;

W_1-2 = mRT ln(V₂/V₁)

For an isothermal process.

For real gases and vapors , the equation of state may be written in a suitable mathematical form , or a table of properties or a property chart may be used.

Joule’s law states that the internal energy of a perfect gas is a function of its temperature only. In a simple system comprising a gas , the perfect gas assumption is used and , taking specific heat at the constant volume , C_v to be constant ,

U₂ – U₁ = m(u₂ – u₁) = mC_v(T₂ – T₁)

(for a gases with variable specific heat , a formula for C_v or a table of properties will be used.)

The specific heat at constant pressure , C_p is given by ;

C_p = C_v + R

The ratio of specific heats ,

  γ = C_p / C_v

(γ is taken as constant in many gas process.)

Solids and liquids are much less compressible than gases and their expansion due to heat is also smaller. Often , we neglect their change in volume and their internal energy is considered to be a function of temperature only.

Vapours are gaseous substances that are easily liquefied by compression. In engineering , we deal with vapour containing droplets of liquid. Here , the liquid and vapor parts are in equilibrium. For a pure chemical substance , there is a unique relationship between the pressure and temperature under such conditions. So , we need a property besides temperature or pressure to know the state. No such property is easy to measure in practical situations. A special property called dryness fraction (symbol x) is used for a pure substance that is part liquid and part vapour (wet vapor).

Steam with water droplets is wet steam. Steam at saturation temperature without water is dry saturated steam or saturated steam. Water at saturation temperature is saturated water.

Properties of wet steam like volume (V , v) , internal energy (u , U) , enthalpy (H , h) and entropy (S , s)can be given in the form ;

ɸ = (1-x) ɸ_f  +  x ɸ_g

Where ɸ is the property of the wet steam and subscripts f and g refer to the saturated liquid and saturated vapor.

Vapor at temperature higher than saturation temperature is super-heated vapor. Other properties are given in the tables as functions of temperature and pressure.

Liquid at temperature less than saturation temperature is sub-cooled liquid. Properties of liquid can be taken to be approximately those corresponding to saturated liquid at the temperature of the liquid.

Properties of pure substances

Pure substance :

A substance that has a fixed chemical composition ; could be a single chemical element or compound of few elements.

Eg : nitogen , oxygen , water

A mixture of various chemical elements or compounds also qualifies as long as the mixture is homogeneous.

Eg : Atmospheric air-mixture of gases and water vapour , but composition remain same everywhere , homogeneous.

A mixture of two or more phases of a pure substance is still a pure substance.

A mixture of oil and water is , however , not a pure substance as the composition at difference places would be different.

Phases of a pure substance: 

Substances exist in different phases , for example , at a room temperature and pressure , steel is in solid form , mercury is in liquid form and nitrogen in gaseous form.

principal phases-solid , liquid and gas with distinct molecular structures. 

However , a substance may have several phases within a principal phase , each with different molecular structure.

Eg : Carbon in solid phase may exist as graphite or diamond.

       Iron has three solid phases (alpha , gamma , delta).

       Helium has two liquid phases(Helium 3 , Helium 4).

       Ice may exist at seven different phases at high pressure.

A phase is identified as having a distinct molecular arrangement that is homogeneous throughout and separated from other phases by easily identifiable boundary surface.

Eg. Two faces of H₂O iced water , where the boundaries are easily identifiable.

Molecular bonds are the strongest in solids , and the weakest in gases.

The molecules in a solid are arranged in three dimensional pattern (lattice) and repeated throughout the solid. Molecules in a solid do not move relative to each other , but continuously oscillate about their equilibrium positions ; velocity of oscillation depends on temperature.

At sufficiently high temperatures , the velocity and momentum of molecules partially overcome inter-molecular forces , and molecules break away , starting of melting process-liquid phase. In liquid phase , the molecular spaces may not be much different to those of solid phase , but they do not have fixed positions relative to each other.The distances between molecules generally increase slightly as a solid turns to liquid , but water is rare exception.

In the gas phase , the molecules are far apart from each other , and there is no order of arrangement. Molecules in gas phase are at a considerably higher level of energy than they are in liquid or solid phases. Therefore a gas must release a large amount of its energy before it can condense or freezes.    

Phase change process of pure substances:

There are many practical situations where two phases of a pure substance coexist in equilibrium.

Eg. Liquid and vapour coexist in the boiler and the condenser of a steam power plant. 

      Liquid and vapour coexist in the freezer (evaporator) of a refrigerator.

Since all pure substances exhibit same general behavior during phase change , water is used to demonstrate the basic principals involved.

Compressed liquid and saturated liquid: 

Consider water at 20^°C and 1 atm pressure ; under these conditions water exist in the liquid phase , and it is called sub-cooled liquid or compressed liquid ; meaning that it is not close to vaporize .         ( figure 9 , state1)

If heat is added and the temperature of water increased up to 100^°C  , when the water is still in liquid form and is about to vaporize , it is called saturated liquid. (figure 9 , state 2) 

Figure 9 : Phase change process of water.

Saturated vapour and superheated vapour:

Further addition of heat to saturated liquid initiates boiling , temperature rising will stop until all the water is vaporized( increase of volume ). The resulting vapour when all the liquid is boiled out will be at the same pressure as of liquid and at a temperature of 100^°C , which is identified as saturated vapour or in other word vapour which is about to condense is called saturated vapour (figure 9 , state 4). Even a small loss of heat causes this vapor to condense.

Once the phase change is completed further addition of heat increase both the temperature and specific volume of vapour (steam). Slight reduction of temperature will not cause condensation. This vapour is called super-heated vapour.

The Second law of Thermodynamics and Air standard cycles

Cyclic processes:

A cyclic process is a single process or a series of processes arranged so that at the end of the cycle the system is at original state. The properties of the system will be the same at the start and the end of the cycle. 

Thus , for a cyclic process ;

 Q + W = 0 = ΔU

This may also be written as ,

 φ dQ + φ dW = 0

Cyclic processes are used in heat engines to convert heat into work. Some cycles are of special importance to heat engines. 

Air standard cycles:

Cycles that are suited for using air as the working fluid are known as air standard cycles. Three air standard cycles will be dealt with here and the cycles will be described in this section.

Since the purpose of an engine cycle is to convert heat into work , its suitability to do that task is measured in terms of thermal efficiency ; 

η_thermal = -W_net / Q_in 

Here ,

-W_net (= -φ dW) is the net work coming out of the system(really , the working fluid of the engine).

Q_in is the sum of all heat added to the system( Sum of all positive heat interactions between the system and surroundings). 

The thermal efficiency of an air standard cycle is known as its air standard efficiency (η_{air standard}) or called after the name of the cycle , as Otto efficiency (η_Otto) , Diesel efficiency (η_Diesel) etc.

The Otto cycle consists of four processes carried out with a perfect gas (in this case air) ;

1. The air is compressed adiabatically by a ratio r.
2. Heat is added at constant volume until the air reaches a suitable temperature and pressure.
3. The air is expanded adiabatically to its original volume.
4. The air is cooled at constant volume to its original state.     

The net work output (= -φ dW) can be found by finding the work done during the processes 1-2 and 3-4 (As no work is done during the other two processes).

On the other hand , heat is given to the air only during process 2-3 and rejected during process 4-1 . The net work can be found more easily as ;

  -φ dW = φ dQ = Q_2-3 + Q_4-1

The air standard efficiency ;

                                                          η_Otto = ( Q_2-3 + Q_4-1 ) / Q_2-3

This value is depends on the compression ratio , r (=V₁/V₂) only and is given by ;

η_Otto = 1 - (1/r^γ-1)

The Diesel cycle differs from the Otto cycle in that heat is added to the air at constant pressure.

Heat is added until the volume increases from V₂ to V₃ . If the compression ratio (V₁/V₂) is r and the ratio V₃/V₂ (known as the cut-0ff ratio) is α , the standard efficiency can be calculated in a way similar to that before to give ;

η_Diesel = (1 - 1/r^γ-1) [ (α^γ – 1) / γ (α – 1) ]

The carnot cycle is the most important thermodynamic cycle in many ways and comprises a pair of adiabatic processes (1-2 and 3-4) and a pair of isothermal  (2-3 and 4-1) processes. As two processes are adiabatic , heat interaction takes place only during the two isothermal processes.

The following equations can be written for the two adiabatic processes ; 

p₁V₁^γ = p₂V₂^γ

and ;

p₃V₃^γ = p₄V₄^γ

For the two isothermal processes ;

   p₂V₂ = p₃V₃

And ;

 p₄V₄ = p₁V₁

Using these four equations we can show that ;

V₂ / V₁ = V₃ / V₄

The net work output may be obtained by calculating the work done during each of the four processes or as ;

-φ dW = φ dQ = Q_2-3 + Q_4-1

In an isothermal process a-b for a perfect gas , the heat supplied ;

Q_a-b = -W_a-b = mRT_a ln(V_b / V_a)

And ;

 V₂ / V₁ = V₃ / V₄

Using these , it can be shown that the efficiency of the Carnot cycle ;

η_Carnot = (1 – T₂/T₁)

The Second law of Thermodynamics:

The second law of thermodynamics is the most powerful law of the physics and has been stated in different ways , which are equally valid and useful in their own way. Engineers find the following statements very useful.

Kelvin-planck statement of the second law:

It is impossible for a device that operates on a cycle to exchange heat with just a single reservoir and produce a net amount of work.

This means that a perpetual motion machine of the second kind (PMM2) , i.e. a machine that takes heat from a single heat reservoir and coverts all of it into work , is not possible. In other words , the working fluid of the engine needs to exchange heat with a heat source and a heat sink (usually the environment). 
It also means that no heat engine can have a thermal efficiency of 100%. 

Clausius statement of the second law:

It is impossible to construct a device that operates on a cycle to produce no effect other than the transfer of heat from a lower-temperature body to a higher-temperature body.

The second law also tells us that the efficiency of an irreversible engine cannot be more than that of a reversible engine operating between the same two thermal reservoirs.

It also tells us that the efficiencies of all reversible engine , we need to understand the meaning of thermodynamic reversibility(reversibility from here on).

Reversibility:

A process is reversible if it is possible to fully reverse the direction of the process and reserve each of its effects on the system(or systems) concerned and restore the system(or systems) to the initial state.

All fully resisted processes are reversible in themselves. If a process involves motion against solid friction or viscous forces , the flow of electrical current against a resistance , Plastic bending , mixing of fluids at different pressures or at different temperatures or of different chemical composition , non-equilibrium chemical reactions , inelastic collision , electric discharge across a voltage difference , and heat flow between bodies with a temperature difference are among common irreversible processes.

Reversibility requires frictionless motion between sliding surfaces , in-viscid fluid motion , elastic deformation and elastic collision of solids , electric current flow against zero electrical resistance , equilibrium reaction between chemicals , transfer of charges without potential difference , transfer of heat without a difference in temperature. 

While each process in a thermodynamic cycle of a simple thermodynamic system may be reversible , interactions with the surroundings can be irreversible. for example , when heat is exchanged with another system at a different temperature.

If we compare engines exchanging heat with a hot reservoir at temperature T_h and a cold reservoir at T_c  , the maximum temperature during the cycle cannot be more than T_h and the minimum temperature cannot be less than T_c.

The working fluid of a Carnot engine receives heat only at T_h and rejects heat only at T_c.

The working fluid in an Otto or a Diesel cycle receives heat while the temperature increases from a value less than T_h until it reaches T_h , it loses heat while the temperature decreases from a value more than T_c until it reaches T_c.

Thus the heat interactions between the working fluid and the two reservoirs are irreversible. Thus η_Otto and η_Diesel will be less than η_Carnot for cycles operating between the same temperature limits.

An absolute scale of temperature can be defined on the basis of reversible engines using the formula ;

η_rev = (1 – T₂ / T₁)

Measurement of the efficiency of a reversible engine operating between two temperatures , of which one is known (or defined) allows us to determine the other. Thus , the second law allows us to define a temperature scale that is independent of the working fluid. In practice this scale coincides with the perfect gas scale of temperature.

Clausius inequality:

For a system undergoing a cyclic process ;

 φ dQ / T ≤ 0

The equal sign applies for reversible processes only. From this , we arrive at a property called entropy.

Entropy:

Change in entropy( Symbol S , specific entropy s ) of a system undergoing a reversible process 1-2 is given by ; 

S₁ – S₂ =  ₁∫² dQ/T

The difference in entropy between two states of any system can be found by identifying a combination of reversible processes that will take the system from one state to the other. It is not permissible to use the above expression or the forms ;

dS = dQ / T   and   dQ = T dS 

for an irreversible process.(note that same rule applies for dW = -p dV)

Many more useful results come from the Second law. A particularly useful result that follows from Clausius inequality is that the entropy of an isolated system can either remain the same or increase.

It can also be said that if a system with work interactions has no heat interaction its entropy will remain the same or increase.

This rule can be used to test the reversibility of a process in a more general way , if for a process ;

If ,   S₂ – S₁ = ₁∫² dQ / T    ; The process is reversible.

If ,   S₂ – S₁ > ₁∫² dQ / T    ; The process is irreversible.

If ,   S₂ – S₁ < ₁∫² dQ / T    ; The process is not possible.

Vapour power cycles : The Rankine cycle:  

The operation of the Carnot cycle with a gas has practical limitations. Vapour at saturation conditions allows heat interactions without to change of temperature. (This is due to the interdependence of pressure and temperature at saturation.)

Thus a vapour operated Carnot cycle is possible with two constant pressure processes and two adiabatic processes arranged inside the vapour dome. Practical considerations make it necessary to deviate from the Carnot cycle and use instead the Rankine cycle. The Rankine cycle is shown below as P-V and T-S plots. 

                           

                           

The Rankine cycle is executed as a series of flow processes and the work done in the turbine is        (h₂ – h₃) for unit mass flow. The heat supplied is (h₂ – h₁) per unit mass flow. The cycle is analyzed using the steam tables. The expansion 2-3 is adiabatic reversible and S₂ = S₁. The feed-pump work is neglected so that h₁ = h₄ , and the net work is the turbine work.

Rankine efficiency ;

η_Rankine  = (h₂ – h₃) /  (h₂ – h₁)

Flow Processes

Processes in Open Systems:

Open systems involve mass flow across the boundary . The closed system can be considered as a special case of an open system with no mass flow across the boundary. Open systems can have work and heat interactions across the boundary and in addition have matter flowing across the boundary. They can be subjected to all the processes that closed systems can be subjected to. Process carried out on matter in flow are called flow processes. It should be noted that it is not possible to talk about an equilibrium state in an open system with mass flow since the matter inside the system is always changing.

The Equation of Continuity:

Consider the open system within the control volume CV in figure2 below ;

Matter is crossing the control surface( the system boundary) at n locations. Let us call each of these flows as a stream and use the suffix i to identify the ith stream. In keeping with our sign convention for boundary interactions , we will attach a plus(+) sign to the mass of matter entering and a minus(-) sign to the mass of matter leaving. By conservation of matter , we can say that the change in the mass(M) of the system over a small interval of time δt is given by ;

 δM = ∑ δm_i

Where δm_i is the mass entering the control volume along stream i. For a finite interval of time from t₁ to t₂ , we may write ;

M₂ - M₁ = ∑ m_i

Where m_i is the mass entering the control volume during the time interval  t₁ to  t₂ along stream i. The above equations are two forms of the Equation of Mass Continuity or simply the Equation of Continuity.

Application of the first law to Open systems:

By considering the matter crossing the boundary of the open system over a small interval of time δt_i we can define a closed system whose boundary changes from CS1 to CS2 (see figure 3).

Let us consider the matter of mass δm_i crossing the boundary of the open system along stream i. If the specific volume of the matter is v_i the boundary expansion during time δt is (v_iδm_i). If the local pressure at the stream is p_i , the boundary expansion work done by the surroundings on the system is p_iv_iδm_i. The product pv is commonly referred to as ‘work of introduction’ or ‘flow work’ in flow processes and represents the work done in transferring a unit mass across a control surface. The total flow work is given by ;

∑ p_iv_iδm_i

If there are heat and work interactions of δW and δQ across the system boundary and each stream has in addition to internal energy , kinetic and potential energy , using the First law we may write ;

E + δE = E + δQ + δW + ∑ p_iv_iδm_i + ∑(u_i + c_i²/2 + gz_i) δm_i

Where E and (E + dE) refer to the total energy within the control volume at times t and (t + dt) , respectively , where ;

E = U + E_k + E_p

Above equation may be rewritten as ;

δE = δQ + δW + ∑ p_iv_iδm_i + ∑(u_i + c_i²/2 + gz_i) δm_i

where u_i is the specific internal energy and c_i the velocity of the fluid in stream i , z_i is the elevation of stream i and g is the local acceleration due to gravity. The sum (p_iv_i + u_i) is a function of , the state of the fluid in stream i and it is therefore a property of the fluid. We use the symbol h to denote it and call it specific enthalpy.

h = u + pv 

For given mass m , the enthalpy is ;

H = mh

And we may write ;

H = U + pV

Above equation can be rewritten as ;

δE = δQ + δW + ∑(h_i + c_i²/2 + gz_i) δm_i

Where the changes in the values of the kinetic and potential energies of the open system are negligible, we may write above equation as ;

δU = δQ + δW + ∑(h_i + c_i²/2 + gz_i) δm_i

The Steady Flow Energy Equation:

An open system can be said to be under steady conditions when the state at any point within it does not change with the time. This means that the mass and the total energy of the open system remain constant.

Equations   δM = ∑ δm_i   and   H = U + pV   , respectively , become ;

 ∑ δm_i = 0

And ;

δQ + δW + ∑(h_i + c_i²/2 + gz_i) δm_i = 0

Above equation is known as the Steady Flow Energy Equation (SFEE). The Continuity Equation (CE) and the SFEE for a steady flow process can be written as ;

 ∑ m_i = 0

Q + W + ∑(h_i + c_i²/2 + gz_i) m_i = 0

For a finite interval of time.

They may be also written as ;

 Q̇ + Ẇ + ∑(h_i + c_i²/2 + gz_i) δṁ_i = 0

Where the dot placed above each of the symbols m , Q ,W refer to differentiation with respect to time. 

( ṁ = dm/dt = mass flow rate ; Q̇ = dQ/dt =heat flow rate ; Ẇ = dW/dt = power supplied )         

The First law of Thermodynamics

Early experimental findings:

we are aware of the experimental observation that both stirring and the application of a burner flame can result in the increase of temperature of a breaker of water. The temperature of the water which goes up as        a result of the transfer of stirring work can be restored to its initial value by a negative heat transfer(or cooling): the magnitude of the negative heat transfer is equal to the heat which can produce the same rise in temperature as the stirring work. Another experiment reported in the literature involves the raising of the  temperature of a given stream of water by a measured amount with an electrical heater which consumes power at a known rate. By such experimental means it was shown that a work transfer of 4.1868 J can raise the temperature of 1g of water by 1°C . The constant of proportionality between work and heat so determined was known as the 'mechanical equivalent of heat'.This is a recognition of the fact that work and heat are quantities of a similar nature. 

We know that mechanical work can be converted to heat by the action of friction , inelastic impact and viscosity. Electric resistance causes the conversion of electrical work to heat. We will soon find that other forms of work can also be converted to heat. The quantitative relationship between work and heat led to the First law of Thermodynamics. 

The first law of Thermodynamics:

Experiments with closed systems which undergo cyclic processes enable us to draw the following conclusion.

When a closed system undergoes a cyclic process , the algebraic sum of the work transfer to it is equal to the algebraic sum of the heat transfer to it.

The above statement is not a logical deduction from other more general and broad propositions regarding the physical world , but no experience has ever contradicted it. Hence it is considered to be a law of nature.This statement , known as the First law of Thermodynamics is one of the bases (singular , basis) of the science of classical Thermodynamics. 

Using our notation that both the work done on the system and the heat supplied to the system are positive , the above can rewritten as ;

dQ + dW = 0 

Perpetual Motion Machine of the First kind (PMM1):

A system which works in a cyclic process and produces a net output of a work (W negative) while having a zero net heat transfer is called a perpetual motion machine of the first kind. We will soon discover that the First law implies that a PMM1 is not possible.

Energy of a system:

There exist a property of a system , called energy(E) such that the change in its value during a process is equal to the difference between the transfers of heat and work.

A Lemma

If Φ is a property of a system , then the change in Φ during a process 1-2 depends only on the states 1 and 2 and not on the nature of the process. Conversely , if there is a magnitude Ψ related to a system such that Ψ changes during a process 1-2 by an amount which depend only on the end states 1 and 2 , then Ψ is a property of the system.

In a cyclic process the net change in a property Φ is zero. Again if we can find a quantity Ψ which shows no net change during a cyclic process then Ψ is a property.

Proof : Let the system under go a cyclic process.(see figure)

If the system follows path 0A1B0 to make a cycle ;

Φ_B dΨ = ₀ ∫¹_~A  dΨ + ₁∫⁰_~B dΨ = 0

If we return to 0 by another path C instead of of B , then ;

Φ_C dΨ = ₀ ∫¹_~A  dΨ + ₁∫⁰_~C dΨ = 0

Hence;

  ₁∫⁰_~B dΨ =   ₁∫⁰_~C dΨ

That is , the change of Ψ during a process does not depend on the details of the process but simply on the end states.
We have quantity E which does not undergo a net change during a cyclic process. By the preceding lemma , E is a property of the system.
Energy is an extensive property ; and it is a consequences of the First law. From the point of view of the First law what interests us is the change in energy of a system and not the absolute value of the energy. In general , the energy E of a system can be expressed as ;

E = U + E_k + E_p + E_s + E_c +E_e + E_m

Where U is internal energy ,  E_k is kinetic energy , E_p is potential energy , E_s is strain energy , E_c is surface energy , E_e is electrical energy , E_m is magnetic energy.
It will be shown later that the energy associated with the molecular structure which can be released by chemical reactions , can be included in the internal energy. Again , let us emphasize that internal energy is not the same as heat. 

The simple system:

When the effects of the gravity , motion , elasticity , electricity , magnetism , surface tension etc. are either absent or insignificant , a thermodynamics system is said to be simple. The energy of a simple system is only in the internal energy mode. System composed of gasses , vapors and liquids fall in to this category. For a simple system , the first law may be stated as ; 

dU = dW + dQ 

or , for a finite process from a state 1 to state 2 , as ;

U₂ – U₁ = W_1-2 + Q_1-2

Internal energy of a system:

Internal energy is the mode of energy associated with the increase in temperature of a system. It is the mode of energy which can be directly affected by heat transfer. However , we shall use the term Internal Energy to signify a particular component of the total Energy , as outlined earlier. Remember that the First law is more than a mere definition of the internal energy by a statement to the effect that it is a thermodynamic property. It states that internal energy is a quantity different in kind from work and heat. Internal energy , being a property , can be said to exist in the system and it can be increased or decreased by a change of state. It is only energy which can truly be said to cross the boundary of a closed system , and the terms work and heat simply refer to two different causes of the flow of energy. In a simple thermodynamic system , the flow of energy which occurs at a result of the movement of a force at the boundary it is termed work , and if it occurs because of a temperature difference between the system and the surrounding it is called heat. The units of Q , W and U are the same in the SI.

It is important to notice that the energy equation concerns changes in internal energy. The First law suggests no way of assigning an absolute value to the internal energy of a system at any given state. For practical purposes , however  , it is possible to adopt some reference state , say 'state 0' , at which the energy , when the system proceeds from this reference state to a series of states 1 , 2 , 3 etc. The internal energy of a closed system remains the same if the system is isolated from its surroundings. A perpetual motion machine of the first kind is thus impossible. ( The perpetual motion machine was originally conceived as a purely mechanical device which , when once set in motion , would continue to run ever. Such a machine would be of no practical value , and we know that , in any case , the presence of friction makes it impossible. What would be of immense value is a machine producing a continuous supply of work without absorbing energy from the surroundings ; such a machine is called a perpetual motion machine of the first kind. The First law implies that a perpetual motion machine of the first kind is impossible.)