# Laws of Thermodynamics

### Zeroth and First Laws of Thermodynamics

The zeroth law of thermodynamics states that when two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other. The first law of thermodynamics states that the total energy of a system is constant.

Four laws of thermodynamics exist. The zeroth law of thermodynamics, developed after the other laws, states that when two thermodynamic systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other. A thermometer is considered a third system. This is helpful for comparing systems to one another. For example, consider three systems: a glass of ice water, the surrounding room, and a thermometer. The temperature of water with ice in it is measured using the thermometer. The temperature rises on the thermometer as the glass of ice water obtains thermal equilibrium with the surrounding room.

The first law of thermodynamics, also called the law of conservation of energy, states that energy cannot be created or destroyed, only transformed from one type of energy to another type of energy. In any change in the state of a system, some energy produces work, the energy transferred when a force acts on an object, and some is transferred to the surroundings or put into the system as heat. Energy is not created or destroyed; it is merely dispersed. In other words, the total energy of the universe is constant. This law of thermodynamics forbids perpetual motion machines, in which the work done by a system is greater than or equal to the energy input into the system. However, no isolated system can be 100% efficient. Some heat energy will always be lost to the surroundings.

### Second Law of Thermodynamics

The second law of thermodynamics states that total entropy of an isolated system only increases over time.

The second law of thermodynamics states that the total entropy of an isolated system only increases over time. All isolated systems tend toward an equilibrium state in which entropy is at a maximum value. Thus, ${\Delta S_{\rm{univ}}}={\Delta S_{\rm{sys}}}+{\Delta S_{\rm{surr}}}$ and $\Delta S_{\rm{univ}}>0,$ for spontaneous processes. At this point, no energy is left to do work. In terms of thermal energy, this law can be thought of as stating that heat does not flow from a colder region to a hotter one spontaneously.

Most systems are only isolated when considering them theoretically because even insulated systems still exist within surroundings. However, the universe can be considered an isolated system, and it has no surroundings with which to interact. Thus, the universe should be tending toward a maximum state of entropy in which no more energy to do work can exist. The ability for enthalpy to increase is greater if heat is absorbed by the system and if the system is more ordered (low temperature). Therefore the change in enthalpy is proportional to $\Delta{H}_{\rm{sys}}$ and inversely proportional to T. This leads to $\Delta S_{\rm{surr}}=-\Delta {H}_{\rm{sys}}/T.$

In chemistry a system is considered isolated if zero energy is entering or leaving the system, which means no mass, heat, or work transfer. The system is considered closed as long as no mass enters or leaves the system and the system is not subject to forces from outside the system. Thus, a beaker in which a chemical reaction between two liquids takes place can be considered a closed system because no mass is being transferred into or out of the system and the only work is being done within the system itself. It would not be considered an isolated system because heat is gained or lost in the chemical reaction.

### Third Law of Thermodynamics

The third law of thermodynamics states that the total entropy of a system approaches a constant value as the temperature of the system approaches absolute zero.

The third law of thermodynamics states that the total entropy of a system approaches a constant value as the temperature of the system approaches absolute zero. Absolute zero is the minimum possible temperature theoretically achievable, equal to 0 K (–273.15°C), at which there is no particle motion. A crystal, a highly ordered microscopic structure, of an element in its most stable form can be considered a system and can be used as a reference for the motion of matter in different states and at different temperature. Thus the third law of thermodynamics allows for the creation of an absolute scale of entropy.

The entropy of one mole of a substance under standard state conditions, expressed in units J/(K mol), is its standard entropy (S°). A standard state is a set of specific conditions under which enthalpies and entropies are measured, typically 0°C and 1 atm pressure. A standard entropy is typically described as a standard molar entropy, which is the standard entropy per mole of a substance. The standard molar entropies of most common substances have been calculated.

Standard entropy can be used to calculate the change in entropy of a chemical reaction. The change in entropy for a reaction ($\Delta S_{\rm{rxn}}$) is the difference between the entropies of the products ($\Sigma S_{\rm{prod}}$) and reactants ($\Sigma S_{\rm{reac}}$).
$\Delta S_{\rm{rxn}}=\Sigma S_{\rm{prod}}-\Sigma S_{\rm{reac}}$
For example, the decomposition of hydrogen peroxide forms water and oxygen gas: $2{\rm {H}_{2}{O}_{2}}(l)\rightarrow 2{\rm {H}_{2}{O}}(l)+{\rm O}_{2}(g)$. The change in molar entropy for this reaction can be calculated. Standard molar entropies are as follows: ${\rm {H}_{2}}{\rm {O}_{2}}=232.95\;{\rm J/K}{\cdot}{\rm{mol}}$, ${\rm {H}_{2}{O}}=188.84\;{\rm J/\rm K{\cdot}\rm{mol}}$, ${\rm {O}_{2}}=120.15\;{\rm J/\rm K{\cdot{mol}}}$.
\begin{aligned}\Delta{S}&={(2(188.84\;\rm{J}/{K{\cdot}mol}\;+120.15\;{\rm J/K{\cdot}mol})\;-2(232.95\;\rm{J/K{\cdot}mol}))}\\&=31.93\;\rm{J/K\;mol}\end{aligned}