First Law of Thermodynamics

 

 

First Law of Thermodynamics 

The first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and thermodynamic work for a system of a constant amount of matter.

 

 

Introduction:

As we all know energy neither can be created nor destroyed, it is just transformed from one form to another. This is called 'Law of conservation of energy '.The first law of thermodynamics is just an upgraded form of the law of conservation of energy. Energy is observed in various forms but basically the energy is subdivided into two types i.e heat energy and thermodynamic work. 

The first law of thermodynamics is formulated by 

∆U=Q - W,

Wherein ∆U denotes the change in internal energy of a closed system. Q denotes the quantity of energy supplied to the system as heat and W denotes the work done.

 

 

For example ,

1) Human metabolism is the conversion of food into heat transfer, work, and stored fat.The whole process is completed in the nucleus. Metabolism is an interesting example of the first law of thermodynamics. 

2) Imagine someone putting an ice cube into a glass of warm water and then forget to drink the it. An hour or two later, they will notice that the ice has melted but the temperature of the water has been cooled. This is because the total amount of heat in the system has remained the same. 

 

History:

In early eighteenth century, French philosopher and mathematician Émilie du Châtelet made notable contributions in field of energy and thermodynamics by proposing a form of the law of conservation of energy by including  kinetic energy. 

 

              In 1840, Germain Hess stated a conservation law (Hess's Law) for the heat generated during chemical reactions. This law was later recognized as a consequence of the first law of thermodynamics, but Hess's but it has some drawbacks and that was reason he didn't got the credit for giving the first law of thermodynamics. 

                  The first full statements of the law came in 1850 from Rudolf Clausius, and from William Rankine. Some scholars consider Rankine's statement less accurate than that of Clausius.

 

The first explicit statement of the first law of thermodynamics, by Rudolf Clausius in 1850:

 

In all cases in which work is produced by the agency of heat, a quantity of heat is consumed which is proportional to the work done; and conversely, by the expenditure of an equal quantity of work an equal quantity of heat is produced.

 After the number of researches the revised statement given by the researchers is :

 

For a closed system, in any arbitrary process of interest that takes it from an initial to a final state of internal thermodynamic equilibrium, the change of internal energy is the same as that for a reference adiabatic work process that links those two states. This is so regardless of the path of the process of interest, and regardless of whether it is an adiabatic or a non-adiabatic process. The reference adiabatic work process may be chosen arbitrarily from amongst the class of all such processes.

 

This statement is not much close to the empirical basis than are the original statements,Largely through the influence of Max Born, this statement is theoretically preferable because of this conceptual parsimony.

Basing his thinking on the mechanical approach in 1949, he proposed revised definition of heat. In particular, he referred to the work of Constantin Carathéodory, who had in 1909 stated the first law without defining quantity of heat. His defination mainly focused on transfer of energy neglecting the transfer of matter, and is mostly preffered .Born notes that when matter is transferred between two systems, internal energy that cannot be broken down into heat and work components is also transferred. There may be connections to other systems that are geographically apart from those of matter transmission and that provide simultaneous and independent heat and work transfer with matter transfer. These transfers conserve energy.

 

Cylic process:

 

Clausius provided two formulations of the first law of thermodynamics for a closed system. The system's inputs, outputs, and cyclical processes were all mentioned in one way, but not changes to the system's internal state. The alternative strategy did not anticipate the process to be cyclical and instead pointed to a gradual change in the system's internal state.

 

A cyclic process is one that can be carried out repeatedly and endlessly, bringing the system back to its starting point. The net work completed and the net heat absorbed (or "consumed," in Clausius' terminology), by the system, are of special interest during a single cycle of a cyclic process.

 

 

 

Sign conventions:

 

In a general process, the net energy added as heat to the system less the thermodynamic work performed by the system, both measured in mechanical units, equals the change in the internal energy of a closed system. Taking  as change in internal energy.

where  denotes the net quantity of heat supplied to the system by its surroundings and  denotes the net work done by the system. This sign convention is implicit in Clausius' statement of the law given above. It originated with the study of heat engines that produce useful work by consumption of heat; the key performance indicator of any heat engine is its thermal efficiency, which is the quotient of the net work done and the heat supplied to the system (disregarding waste heat given off). Thermal efficiency must be positive, which is the case if net work done and heat supplied are both of the same sign; by convention both are given the positive sign.

Nowadays, however, writers often use the IUPAC convention by which the first law is formulated with thermodynamic work done on the system by its surroundings having a positive sign. With this now often used sign convention for work, the first law for a closed system may be written:

 

Continuing in the Clausius sign convention for work, when a system expands in a quasistatic process, the thermodynamic work done by the system on the surroundings is the product, , of pressure, , and volume change, , whereas the thermodynamic work done on the system by the surroundings is . Using either sign convention for work, the change in internal energy of the system is:

 

 

where  denotes the infinitesimal amount of heat supplied to the system from its surroundings and  denotes an inexact differential.

where  denotes the infinitesimal amount of heat supplied to the system from its surroundings and  denotes an inexact differential.Thus the term 'heat' for  means "that amount of energy added or removed as heat in the thermodynamic sense", rather than referring to a form of energy within the system. Likewise, the term 'work energy' for  means "that amount of energy gained or lost through thermodynamic work". Internal energy is a property of the system whereas work done and heat supplied are not. A significant result of this distinction is that a given internal energy change  can be achieved by different combinations of heat and work. (This may be signaled by saying that heat and work are path dependent, while change in internal energy depends only on the initial and final states of the process. It is necessary to bear in mind that thermodynamic work is measured by change in the system, not necessarily the same as work measured by forces and distances in the surroundings;^[25] this distinction is noted in the term 'isochoric work' 

 

Evidence of first law of thermodynamics :

It was empirically observed data, such as calorimetric data, that led to the original induction of the first law of thermodynamics for closed systems. However, it is currently accepted to define work in terms of changes to a system's external properties and to define heat using the law of conservation of energy. The rule was first discovered gradually over a period of maybe fifty years or more, and some of the early investigations were done in terms of cyclic processes.

 

The description that follows describes state changes in a closed system caused by compound processes that aren't always cyclic. This description initially takes into account adiabatic processes (in which there is no heat transfer) and adynamic processes, for which the first law is easily confirmed due to their simplicity (in which there is no transfer as work).

 

 

Applications :

1) Isobaric processes.

The first law of thermodynamics states that any change in the internal energy of a given system (U) will be the same as the difference between the amount of thermal energy added to that system (Q) and the net work that is done by that system (W).
Molar heat capacity is the heat given per mole per unit rise in the temperature of a gas.  If this thermal energy is supplied when pressure remains constant, it is called Molar Heat Capacity at constant pressure. 

This is denoted by

Cp=(△Qn△T)pCp=(△Qn△T)p

, where the subscript ‘p’ denotes constant pressure.

As discussed earlier, the heat supplied to the gas in an isobaric process goes partially in increasing its volume by a small amount (dV) and partially in increasing its internal energy by (dU). 

From the First Law of Thermodynamics,

△Q=△U+△W△Q=△U+△W

.  Applying, we get

(dQ)p = dU + PdV……. (i)

(at constant volume dV = 0, therefore W=0, from the first law of thermodynamics

△Q=△U△Q=△U

or heat supplied at constant volume = change in its internal energy). So, dU = (dQ)v.

Therefore equation becomes,              

(dQ)p = (dQ)v + PdV……. (ii) 

For an Ideal Gas, PV = nRT, 

Therefore,              PdV = nRdT,

So,   (dQ)p = (dQ)v + nRdT……. (iii)

From here we also can prove              

Cp = Cv + R

Dividing (iii) by ndT we get              

(dQndT)p=dQndTv+nRdTndT(dQndT)p=dQndTv+nRdTndT

And as we know,      (dQndT)p=Cp(dQndT)p=Cp

 Similarly,      (dQndT)v=Cv

                          (dQndT)v=Cv

Putting these values, we get,

Cp = Cv +R

2) Adiabatic processes .

 In contrast to this, consider a gas that is allowed to slowly escape from a container immersed in a constant-temperature bath. As the gas expands, it does work on the surroundings and therefore tends to cool, but the thermal gradient that results causes heat to pass into the gas from the surroundings to exactly compensate for this change. This is called an isothermal expansion. In an isothermal process the internal energy remains constant and we can write the First Law

0=q+w

q= –w

This illustrates that the heat flow and work done exactly balance each other.

Because no thermal insulation is perfect, truly adiabatic processes do not occur. However, heat flow does take time, so a compression or expansion that occurs more rapidly than thermal equilibration can be considered adiabatic for practical purposes. If you have ever used a hand pump to inflate a bicycle tire, you may have noticed that the bottom of the pump barrel can get quite warm. Although a small part of this warming may be due to friction, it is mostly a result of the work you (the surroundings) are doing on the system (the gas.)

Adiabatic expansion and contractions are especially important in understanding the behavior of the atmosphere. Although e. we commonly think of the atmosphere as homogeneous, it is really not, due largely to uneven heating and cooling over localized areas. Because mixing and heat transfer between adjoining parcels of air does not occur rapidly, many common atmospheric phenomena can be considered at least quasi-adiabatic.

 

 

3) Isochoric processes.

• The work done is given by dW=Pdv.

• Since in isochoric process dv=0, therefore the work done is also zero.

• From the first law of  thermodynamics we have ,dU=dq+dW.

              dU=dq+0

            Therefore, dU=dq

Since a gas's temperature changes in accordance with its internal energy, a gas will warm up during adiabatic compression and cool down during adiabatic expansion.

Conclusion: 

From the following blog we come to an conclusion that the 'First law of thermodynamic' by various researchers viz. Rudolf Clausis and Max Born states that heat is a form of energy, and thermodynamic processes are therefore subject to the principle of conservation of energy. This means that heat energy cannot be created or destroyed. It can, however, be transferred from one location to another and converted to and from other forms of energy.