Thermal equilibrium is the state when the macroscopic properties of a system do not vary with time. Consider a box with two partitions, separated by a wall, that does not exchange energy. The box is insulated from the outside. When the partition is removed, the gas will mix and exchange energy until the systems attain the same temperature. Heat flows from the hot body to the cold. The state of thermal equilibrium indicates that there is no matter flowing in or out of the system.

Let two systems, A and B, be separated by an adiabatic wall. It does not allow the flow of energy through it. Let both of these be in contact with a third system, C, with A and B connected to it by a conducting wall. After some time, A and B will attain the same temperature as C. The Zeroth Law states that two systems in thermal systems in contact with a third system are individually in equilibrium with each other.

If two bodies have temperature differences, heat flows between them. A system is made up of molecules. The total energy of those particles, combining their potential and kinetic energy, is the system’s internal energy. It is related to the random motions of the molecules, including the rotational and vibrational motions. For a gas, the work done is the product of its pressure and volume. These three properties are innately macroscopic. Heat and work are not state variables, whereas internal energy is a state variable.

The heat provided to a system is used for increasing its internal energy, and the remaining portion is used for work. This conservation principle is written as:

\( \Delta \)Q= \( \Delta \)U + \( \Delta \)W

Where:

\( \Delta \)Q: Heat provided to the system

\( \Delta \)U: Change in internal energy

\( \Delta \)W: Work done by the system for an ideal gas

\( \Delta \)W=P \( \Delta \) V

P : Pressure

V : Volume

We could measure the change in temperature of a body when an amount of heat energy is absorbed or released. The amount of heat required to raise the temperature of a unit mass of a substance by a unit degree Celsius is termed specific heat capacity.  If measured in moles, it is called molar-specific heat.

The following expression will be required for solving problems:

S = \( \frac{\Delta Q}{\Delta T} \)   

Where:

S : Specific heat capacity of the substance

\( \Delta \) Q : Change in heat energy

\( \Delta \) T : Change in temperature

The specific heat under constant pressure is Cp, and that under constant volume is Cv. Both are different for the same materials. According to the Dulong–Petit law and law of equipartition, the specific heat at the constant volume of a solid is 3R.

In equilibrium, the system could be described based on macroscopic properties like pressure, volume temperature, etc. These are the state variables that depend on the present state of the system. A combination of these variables would give rise to an equation capable of describing the state. The equation of state of the ideal gas is:

PV = nRT

P: Pressure

V: Volume

R: Gas constant

T: Temperature of an ideal gas

The main thermodynamic processes are: 

• Quasi-static process: The process in which changes happen in a system so slow that it won’t affect the internal equilibrium is called the quasi-static process.
• Isothermal process: It is a thermodynamic process in which the temperature of the system remains constant.
• Isobaric process: In this case, the pressure of the system is constant.
• Isochoric process: In this case, the volume of the system is constant.
• Adiabatic process: An insulated system in which no heat transfers from the system to the surroundings is called an adiabatic process.
• Cyclic process: The cyclic process is one in which a system returns to its previous state. So, the internal energy is a state variable, becomes zero, and heat supplied will equal to work done.

A heat engine converts heat energy into mechanical work. It has a source that supplies the heat content, a sink that draws the heat, and a working substance that does the work. The work is done by the system using the heat supplied to the system. Efficiency amounts to how much the amount of heat supplied is utilized as work. If the system’s efficiency is 1, all the heat supplied will be converted into work. This is an ideal case. Carnot Engine is an example of such a case.

The efficiency of the heat engine is: 

\( \eta \) =1\( -\frac{T2}{T1} \)

\( \eta \) : Heat capacity

T1: Temperature of the source

T2: Temperature of the sink

Refrigerators work on the reverse concept of heat engines. Here, the working substance gets cooled from the sink and does work on the hot substance. A heat pump is also similar to a refrigerator. The refrigerators cool the surroundings, whereas a heat pump heats it.

Entropy is the measure of the disorderliness of a system. This law suggests that the entropy of a system can never decrease. This is explained in two definitions by Kelvin-Plank and Clausius. An external agency is required to stop the cooling of a hot object.

If any process is reversible to its initial state, then it is called a reversible process. However, all spontaneous events in the universe are irreversible. They cannot be reversed to the initial state.

Carnot’s engine is an ideal heat engine. It is reversible and works in two limits of temperature, where the sink absorbs the heat, and the source provides it. Carnot’s theorem suggests that no other heat engine will have more energy than a Carnot’s engine working in the same temperature limits since the efficiency of Carnot’s engine is 1, an ideal case scenario.

1. Explain the laws of thermodynamics.

A. Zeroth Law: Two systems in thermal equilibrium with a third system are in thermal equilibrium individually with each other. 

First Law: The heat supplied to a system is used for changing the internal energy, and the remaining part is used to do work. This is the law of conservation. 

Second Law: Kelvin-Planck’s statement states that no process is possible whose sole result is the absorption of heat from a reservoir and complete conversion of heat into work.

Clausius' statement: States that no process is possible whose sole result is the transfer of heat from a colder object to a hotter object.

Carnot’s theorem: No engine operating between two temperatures can have an efficiency greater than that of the Carnot engine.

2. What is thermal equilibrium?

A. When a system is in thermal contact with the surroundings and there is still no flow of energy, it is in thermal equilibrium. The system will be isothermal, i.e. have the same temperature. When a system is in thermal equilibrium, its macroscopic properties won’t change with time. The system is in chemical and mechanical equilibrium as well.

3. What are the important topics in thermodynamics?

A. Heat engine, heat capacity, and laws of thermodynamics are important topics in thermodynamics.
A heat engine converts heat energy to mechanical work. An ideal engine is Carnot’s engine.
Heat capacity is the amount of heat supplied to produce a unit temperature variation in a system. The amount of heat required to raise the temperature of a unit mass of a substance by unit degree Celsius is called the specific heat capacity. If it is expressed in moles, it is called molar heat capacity.
The main laws of thermodynamics are the Zeroth Law, First Law and Second Law of Thermodynamics, and Carnot’s theorem.