The Laws Of Thermodynamics

 The Laws Of Thermodynamics

Earlier, heat was thought to be an invisible fluid which filled the pores of a substance. When a hot body body and cold body come in contact, the transfer of this fluid takes place from hotter body to the colder one until both the bodies reach are at same temperature.Since then, it has taken years of thinking and research and many theories to reach our present understanding of heat and temperature.

Thermodynamics is the branch of physics that deals with the concepts of heat and temperature and the inter conversion of heat and other forms of energy. Thermodynamics deals only with macroscopic systems. It is concerned with internal macroscopic state of the system. Before coming to the laws of thermodynamics, we will study what thermodynamic equilibrium is.

1.0 Thermal equilibrium 

 The state of a system is said to be in equilibrium state if the characteristic macroscopic variables of the system do not change. Generally, it depends on the surroundings of the system and the walls that separates the system from the surroundings.

2. 1 Zeroth Law of Thermodynamics 

Suppose there are two systems A and B. An adiabatic wall separates the two. Each system A and B is in contact with a third system C, separated by a conducting wall as shown in fig 2.1a. The states of the systems will change and the systems A and B will eventually come to equilibrium with system C. After this, if the wall separating the Systems A and B is replaced by a conducting wall while the one separating the both of them from C is separated by an adiabatic wall (fig 2.1b), it is observed that there are no variations in the states of systems A and B. In other words they are in thermal equilibrium. This experiment is the basis of Zeroth Law of Thermodynamics. R. H. Fowler stated it as 'two systems in thermal equilibrium with a third system separately are in thermal equilibrium with each other.'

 

Figure 1: Zeroth law of thermodynamics

This law was stated in 1931 after the first and second laws of thermodynamics. Since it was more fundamental, it was named as the Zeroth law of Thermodynamics. It states that when 2 bodies are in the thermal equilibrium, both of them must have a physical quantity with the same value for both. This physical thermodynamic quantity is called as temperature(T). Thus, if A and B each are separately  equilibrium with system C,  T(A) = T(C) and T(B) = T(C). Hence, T(A) = T(B).

 

2.2 Concepts of Heat, Internal Energy and Work

Temperature in simple words can be said as the measure of how hot the body is. The direction of flow of heat when two bodies are in thermal contact depends on temperature. We will look into the concepts of work, internal energy and heat.

Every bulk system comprises of molecules in a huge number. Internal energy is simply the total kinetic and potential energies of all the molecules in the system. This is in reference relative to which the centre of mass of the system is at rest. hence, the internal energy refers to exclusively the energy associated the molecules' random motion in the system. Internal Energy is denoted by U.

Internal energy is dependent on only the state of the system and not on the path through which it is arrived. It is a 'State Variable'- it depends only on specific values that describe state of the system such as pressure, volume and temperature. Consider a system of certain mass of gas contained a cylinder with a movable piston. There are two ways by which we can increase the internal energy of the system. One is to keep the cylinder in a surrounding with temperature higher than the system and let the system heat i.e. increase the system's temperature. The other is to push the piston, decreasing the volume and performing work on the system. The internal energy can be decreased by performing the activities in reverse that is to cool the system or let the gas push the piston outwards i.e. to let the system do the work.

Hence, there are two ways to alter the state of a thermodynamic system and changing its internal energy.

We can say that heat and work are not state variables and rather are the modes of energy transfer to a system resulting in change in internal energy of the system

2.3 First Law of Thermodynamics

We have studied that heat and work are the two modes of altering the internal energy of a system. 

𝚫Q = Heat supplied to the system by the surroundings.

𝚫W = Work performed by the system  on the surroundings.

𝚫U = Variation in the Internal energy of the system.

 Thus, the principle of conservation of energy then implies:

 𝚫Q = 𝚫U + 𝚫W

 This simply means that the heat energy supplied to the system, partially goes in increasing the internal energy of the system and the remaining is used to perform  work on the surrounding.

This is the First Law of Thermodynamics. It is the law of conservation of energy.

If we put the equation in an alternative form,

𝚫Q - 𝚫W = 𝚫U

The change in the system from initial to final state can take place through various paths. Like,  in order to change the state from (P1,V1) to (P2,V2), one can first change volume keeping pressure constant to (P1,V2) and then change the pressure of the gas from P1 to P2, V2 constant to get the final state (P2,V2). Otherwise, we can keep the volume constant and vary the pressure first and then volume. As Internal energy U is a state variable, 𝚫U depends only on the initial and final state. However, 𝚫Q and 𝚫W depend on the path followed to reach the final state. Hence, 𝚫Q-𝚫W is path independent. If the system is taken through a process where the change in internal energy 𝚫U = 0 (for example isothermal expansion of ideal gas),

𝚫Q = 𝚫W

i.e. heat supplied to the system is used up entirely in doing work on the environment.

If the system consists of s cylinder with a movable piston filled with gas , work is done by the gas by moving the system. 

Force = Pressure x Area,

Volume = Area x displacement of piston,

This implies,

𝚫W = P𝚫V

Where 𝚫V is change in volume.

Hence, 𝚫Q = 𝚫U + P𝚫V

Figure 2: First Law of Thermodynamics

 

Thermodynamic Processes 

Imagine a gas which is in thermal and and mechanical equilibrium with he surroundings. The temperature and pressure of the system and the surroundings will be equal. Suppose that the external pressure is suddenly reduced (say by lifting the weight on the movable piston in the container). The piston will accelerate outward. During this process, The system will go through non-equilibrium states. They do not have any well defined pressure and temperature. Similarly, if a temperature difference between the gas and the surroundings is created, the gas will go through non-equilibrium states through exchange of heat. Eventually, the gas will settle to an equilibrium state with well-defined temperature and pressure equal to those of the surroundings. 

Therefore, for convenience, we consider that the system reaches equilibrium at each state, after every small step.Theoretically, this process will be incredibly slow, therefore known as quasi-static process.(almost static). The system changes its variables (P, T, V ) so slowly that it remains in thermal and mechanical equilibrium with its surroundings throughout. In a quasi-static process, at every stage, the difference in the pressure of the system and the external pressure is infinitesimally small. The same is true of the temperature difference between the system and its surroundings. To take a gas from the state (P, T ) to another state (P ′, T ′ ) via a quasi-static process, we change the external pressure by a very small amount, allow the system to equalise its pressure with that of the surroundings and continue the process infinitely slowly until the system achieves the pressure P ′. Similarly, to change the temperature, we introduce an infinitesimal temperature difference between the system and the surrounding reservoirs and by choosing reservoirs of progressively different temperatures T to T ′, the system achieves the temperature T ′.

 

Second law of thermodynamics

We have never seen an object kept on the floor go up in the air although the law of conservation of energy i.e. the first law would allow it.

When a hot and a cold body are kept in contact, the heat flows from the hotter body to the colder body until their temperatures are equal. Does it ever occur that the hot body becomes hotter and the cold one, colder?

Imagine a container with rigid walls divided in two parts by a partition with a valve. one part is filled with gas and the vacuum is created in the other part. When the valve is opened, the gas fills the part with vacuum. Is reverse possible?
In all these phenomena the first law isn't violated but still they don't occur. This is because there are some additional rules which are applied. The second law of thermodynamics forbids many such phenomena which are allowed by the first law of motion.

 

Clausius Statement  of Second Law of Thermodynamics

No process is possible whose sole result is the transfer of heat from a colder object to a hotter object.[]

Reversible and Irreversible processes

Imagine a thermodynamic system which undergoes a process in which it goes from an initial state i to a final state f. The heat absorbed by the system from the surroundings during the process is used to perform work on the environment. is it possible to reverse this process so that both, the system and the surroundings returns to their initial states without affecting any factors? Observations show that this isn't possible for most of the processes in nature. The spontaneous processes in nature are irreversible. Let's take an example of a hot cup of tea left on a table for sometime. The cup eventually cools down and comes to the  room temperature. The reverse is not possible. The surrounding won't get cooler and the cup warmer. This will violate the Second Law of thermodynamics, if it is reversed.  The combustion reaction of a mixture of petrol and air ignited by a spark cannot be reversed. Cooking gas leaking from a gas cylinder in the kitchen diffuses to the entire room. The diffusion process will not spontaneously reverse and bring the gas back to the cylinder. The stirring of a liquid in thermal contact with a reservoir will convert the work done into heat, increasing the internal energy of the reservoir. The process cannot be reversed exactly; otherwise it would amount to conversion of heat entirely into work, violating the Second Law of Thermodynamics. Irreversibility is a rule rather an exception in nature. Since dississipative effects are present everywhere and can be minimized but not fully eliminated, most processes that we deal with are irreversible. A thermodynamic process (state i → state f ) is reversible if the process can be turned back such that both the system and the surroundings return to their original states, with no other change anywhere else in the universe. From the preceding discussion, a reversible process is an idealized notion. A process is reversible only if it is quasi-static (system in equilibrium with the surroundings at every stage) and there are no dississipative effects.[]

 

Entropy:

Entropy is a concept, a physical property that measures the degree of randomness or disorder in any system.
Entropy was first defined in the mid-nineteenth century by German physicist Rudolph Clausius, one of the founders of the field of thermodynamics. He formulated it as the quotient of an amount of heat to the instantaneous temperature, in the dissipative use of energy during a transformation. In German, he described it as Verwandlungsinhalt, which is in essence a transformation-content, and thereby coined the very term entropy from the Greek word for transformation.[]

Entropy is denoted by S.

The Second Law of Thermodynamics can also be expressed in terms of entropy.

dS ≥ 0

Figure 3: Second Law of Thermodynamics

 

 

 

Third Law of Thermodynamics

The third law of thermodynamics states as follows, regarding the properties of closed systems in thermodynamic equilibrium:The entropy of a system approaches a constant value as its temperature approaches absolute zero.

In Layman's terms, this law states that as the temperature approaches zero, the entropy of a perfect crystal of a pure substance approaches zero. No ambiguity is left in the alignment of the perfect crystal as to the location and orientation of each part of the crystal. With the reducing energy of the crystal, the vibrations of the individual atoms are eventually reduced to nothing. As a result, the crystal becomes the same everywhere.

a) Single possible configuration for a system at absolute zero, i.e., only one microstate is accessible. Thus S = k ln W = 0. b) At temperatures greater than absolute zero, multiple microstates are accessible due to atomic vibration (exaggerated in the figure). Since the number of accessible microstates is greater than 1, S = k ln W > 0.

The third law provides an absolute reference point for the determination of entropy at any other temperature. The entropy of a closed system, determined relative to this zero point, is then the absolute entropy of that system. Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times Boltzmann's constant k_B = 1.38×10⁻²³ J K⁻¹.

The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero provided that its ground state is unique, because ln(1) = 0. If the system is composed of one-billion atoms, all alike, and lie within the matrix of a perfect crystal, the number of combinations of one-billion identical things taken one-billion at a time is Ω = 1. Hence:

${\displaystyle S-S_{0}=k_{\text{B}}\ln \Omega =k_{\text{B}}\ln {1}=0}$

The difference is zero, hence the initial entropy S₀ can be any selected value so long as all other such calculations include that as the initial entropy. As a result, the initial entropy value of zero is selected S₀ = 0 is used for convenience.

${\displaystyle S-S_{0}=S-0=0}$

${\displaystyle S=0}$

1. All the fuel powered we use , right from scooters, cars to aeroplanes, they all work on the basis of second law of thermodynamics and carnot cycle irrespective of the type of engine, petrol or diesel.

2. Renewable energy is an important subject area of thermodynamics that involves studying the feasibility of using different types of renewable energy sources for domestic and commercial use.

3. Thermodynamics also deals with heat transfer through conduction, convection and radiation and has an important role in all the industries as well as in electronics.

4. It has a crucial role in working of power plants(thermal, nuclear, etc.). 

 

 

Authors: SY_CHA_B1_Group3

1. (9) Kshitij Borhade

2. (10) Karuna Chandrakapure

3. (12) Pratiksha Chavare

4. (23) Maithili Fiske

 

 

 

 For educational purpose only.

 References:

1. https://www.google.com/url?sa=i&url=https%3A%2F%2Fwww.aetipsandtricks.com%2Fvfx%2Fcreate-this-energized-molecule-effect%2F&psig=AOvVaw0_AZatut2YyU1Nzs3WRbJQ&ust=1608798317755000&source=images&cd=vfe&ved=0CAIQjRxqFwoTCPD0s_zW4-0CFQAAAAAdAAAAABAE 

2. https://en.wikipedia.org/wiki/Entropy

3. https://en.wikipedia.org/wiki/Third_law_of_thermodynamics