The Laws of Thermodynamics

The Laws of Thermodynamics Introduction

Before we begin a discussion of the laws of thermodynamics, we will first define what thermodynamic systems are.

Types of Thermodynamic Systems

There are three different types of thermodynamic systems:

• Open Thermodynamic System - some or all of the material from the surroundings can flow into an open system; heat can also flow across the walls of the container of an open system.

• Closed Thermodynamic System - material from the external surroundings cannot flow into a closed system; however, heat can flow across the walls of the container of a closed system.

• Isolated Thermodynamic System - material from the surroundings cannot flow into an isolated system; heat cannot flow across the walls of the container of an isolated system.

Properties of Thermodynamic Systems

Now, let's dive into the properties of open, closed, and isolated systems.

1. Open Systems:

• Have container walls that exchange heat and particles with the surroundings.

• At thermal equilibrium, an open system does not sustain a temperature difference between itself and the surroundings.

• Allow for the exchange of matter with the surroundings. The container walls of open systems are permeable to at least one, or more, of the chemical substances coming from the surroundings.

Figure 1: Open Thermodynamic System.

2. Closed Systems:

• Have container walls that can exchange heat; cannot exchange particles with the surroundings.

• Closed systems with one type of particle (atom or molecule) will contain a constant number of particles within the container.

• For systems with more than one type of particle, chemical reactions may transform these particles into those with different masses, but the total number of atoms making up these particles will remain constant within the container.

Figure 2: Closed Thermodynamic System.

3. Isolated Systems:

• Have container walls that cannot exchange heat with surroundings; cannot exchange particles with the surroundings.

• Does not interact with the surroundings in any way.

Figure 3: Isolated Thermodynamic System.

The Laws of Thermodynamics Overview

Now that we know that thermodynamics is and the types of systems that exist, let's focus of the laws of thermodynamics. But first, take a look at the definition of thermal equilibrium.

There are four basic laws of thermodynamics:

• The Zeroth Law of Thermodynamics - According to this law, when a closed system at a higher temperature interacts with a closed system at a lower temperature, energy in the form of heat transfers to the closed system that is at a lower temperature until thermal equilibrium is reached.

• First Law of Thermodynamics - The first law of thermodynamics states that the total energy of the universe remains constant.

• Second Law of Thermodynamics - The second law states that the disorder of the universe, a system and its surroundings, always increases for a process that occurs naturally; that is, without the input of external matter or energy into the system.

• Third Law of Thermodynamics - The third law of thermodynamics states that the disorder of a system approaches zero as the temperature approaches zero.

The Laws of Thermodynamics Explanation

Let's explore these laws of thermodynamic a bit more.

The Zeroth Law of Thermodynamics:

Consider the following experiment, you grab two cans of your favorite beverage. You take one can from a freezer and the other you take from atop a picnic table that is exposed to the hot sunshine. You tie these two cans together with some tape and wait for about 30 minutes. What do you think will happen? Will the two cans get hotter, will they both get cooler, or will they come to the same temperature that is somewhere in between?

You probably know the answer already, the cans will come to the same temperature that is somewhere between hot and cold. This observation can be restated in the following way:

• When an object at a higher temperature physically interacts with an object at a lower temperature, the object at a higher temperature transfers energy, in the form of heat, to the lower temperature object.

• In the absence of losses to the environment, the two objects, that are in physical contact, will come to the same temperature.

• The objects are said to be in thermal equilibrium when both come to the same temperature.

Thermal equilibrium is related to the Zeroth Law of Thermodynamics via the following statement,

The First Law of Thermodynamics

Now let's move on to the first law of thermodynamics. But first, some relevant defnitions.

Now it might seem strange to say that, "the total energy of the universe remains constant" according to the first law of thermodynamics. Nevertheless, this statement is always correct and there has never been observed a phenomenon that violates this law in all of the universe. The first law of thermodynamics is also referred to as the law of the conservation of energy and can be stated mathematically as:

$$\Delta{U}=Q-W$$

where,

• ΔU is the change of internal energy in a closed system
• Q is the energy supplied to the system
• W is the amount of thermodynamic work done by the system on the surroundings.

To better understand this, we are going to break down each variable.

1. We note that the law of the conservation of energy (first law of thermodynamics) only concerns the measurement of the difference between the final internal energy, U_f , and initial internal energy, U_i , of a system:

$$\Delta{U}=U_f-U_i$$

• The internal energy difference, ΔU, is calculated between a reference state, U_i, (that is at standard conditions) and a final thermodynamic state, U_f .
• The internal energy difference, ΔU, is an example of a thermodynamic state function.
• A state function depends only on the initial and final states and is not concerned with the path taken by the system in going from the initial state to the final state.

2. The energy supplied to the system, Q, is the energy transferred to the system by the external surroundings. The following table displays the types of energies that come from the surroundings for various thermodynamic systems:

3. The thermodynamic work, W, done by the system on the external surroundings can come from changes in the volume of the system, changes in the temperature of the system that drives another system in the surroundings and pressure increases in the system that are transferred to the other systems in the surroundings.

The Second Law of Thermodynamics:

We begin our discussion of the Second Law of Thermodynamics with a definition of the disorder of a system:

Note: A state function is a mathematical formula that takes a state variable as input and typically also includes equilibrium state parameters and constants. For example, let's consider the ideal gas law, where we want to calculate the temperature change of a thermodynamic system at chemical equilibrium: $$\Delta{T} =\frac{V\cdot \Delta{P}}{nR}$$

Let's further assume that for this particular thermodynamic system the system volume, V , and the number of moles, n , are not changing at equilibrium. Thus, the volume and the number of moles for this thermodynamic state are no longer varying but have become parameters of the system.

This leaves us only the system pressure, ΔP = P_f - P_i, to vary. In this case, the system pressure is the state variable. The state variable, ΔP, is used as input to calculate the state function for the temperature change, ΔT = T_f - T_i . Lastly, that the gas constant is, R. Now let's consider the difference between state functions and process functions:

• A state function only depends on the initial and final states and is not concerned with the path taken by the system in going from the initial state to the final state. Examples of state functions are system temperature, system pressure and volume.

• A process function depends on the path taken from the initial state and the final state. Examples of process functions are the instantaneous heat and instantaneous work.

At this point, we are now able to formulate the entropy of a spontaneous change in an isolated system mathematically:

$$\Delta{S_{tot}}=S_f-S_i\,>\,0$$

where,

• The initial entropy of the surroundings and the isolated system is S_i

• The final entropy of the surroundings and the isolated system is S_f

• The total entropy of the system and the surroundings is, S_tot.

Notice that the entropy difference is a state function. In particular, for isolated systems undergoing spontaneous change the formula for the entropy is equivalent to the Second Law of Thermodynamics.

$$\Delta{S_{tot}}=S_f-S_i\,>\,0$$

There are different forms of the Second Law of Thermodynamics for different systems and different conditions. We will discuss some of these in the "The Laws of Thermodynamics Examples" section.

The Third Law of Thermodynamics:

Finally, we state the Third Law of Thermodynamics:

Some implications of the Third Law of Thermodynamics are:

• When the temperature of a thermodynamic system approaches zero Kelvin the entropy of the system also approaches zero and the movement of particles in the system stops.

• When the entropy of the system approaches zero the kinetic energy of the system approaches zero.

• A system at zero entropy only contains potential energy.

The Laws of Thermodynamics Examples

Now, let's look at some examples involving the laws of thermodynamics.

1. The Gibbs Free Energy: The amount of energy, G , that is free to do work on a thermodynamic system.

The Gibbs free energy equation is applied to thermodynamic systems at chemical equilibrium that are also at constant temperature and pressure. Mathematically:$$G=H-TS$$

where

• The Gibbs free energy is G

• The enthalpy is H

• The system temperature is T

• The system entropy is S.

As with the enthalpy, H , the Gibbs free energy and the system entropy cannot be measured directly. It is only the difference in the Gibbs free energy that can be measured for any system:

$$\Delta{G}=\Delta{H}-T\Delta{S}$$

where,

• ΔG is the Gibbs free energy difference

• ΔH is the enthalpy difference

• T is the system temperature

• ΔS is the system entropy difference. Thus, the Gibbs free energy is a state function.

Now, we may ask, "Why are the laws of thermodynamics important?" Thermodynamics shows that the hydrolysis of ATP releases a large amount of free energy that is used by the body to drive metabolic reactions that maintain the living state.

Laws of Thermodynamics Simplified

To finish off, let's make a table summarizing the laws of thermodynamics in a simplified way.