Thermodynamics is the branch of science that explores how heat, work, and energy interact with each other and how energy is transferred from one form to another. It helps to understand the behavior of matter on a large scale, such as the heating of a house, the workings of engines, or the flow of energy in natural systems, without needing to look at the motion of individual particles. Essentially, thermodynamics explains how energy drives changes in the world around us.
System
A system in thermodynamics is a specific portion of the universe that we choose to study or observe. It consists of a definite quantity of matter or a region in space separated from the rest of the universe by a boundary. This boundary may be real or imaginary, and it can be either fixed or movable depending on the situation. Everything outside the system is considered the surroundings.
A system is homogeneous if its physical and chemical properties are uniform throughout. It is heterogeneous if different parts have different properties. Based on the exchange of matter and energy, systems are classified into three types.
- Open System—An open system is one that can exchange both matter and energy with its surroundings. Mass and energy can enter or leave the system. Eg: hot coffee in an open cup and a steam turbine.
- Closed System—A closed system can exchange energy with its surroundings but cannot exchange matter. Energy may cross the boundary, but mass remains constant within the system. Eg: a refrigerator, a piston cylinder arrangement, or coffee in a sealed steel flask.
- Isolated System—An isolated system is a system that neither exchanges matter nor energy with its surroundings. It is completely sealed and perfectly insulated, so no heat or mass can enter or leave. In practice, a perfectly isolated system does not exist, but the universe is commonly considered an isolated system. Eg: A tightly corked thermos flask containing hot coffee.
Surrounding
The surroundings refer to everything outside the system that can interact with it or influence its behavior. In simple words, whatever is not part of the system but can affect it is called the surroundings.
The system and its surroundings together form the universe. For practical purposes, surroundings usually mean the nearby region around the system that can exchange energy or matter with it.
Branches of Thermodynamics
- Classical Thermodynamics- The behavior of matter using a macroscopic approach. It deals with bulk properties such as temperature, pressure, and volume to analyze systems and predict their behavior during physical or chemical processes.
- Statistical Thermodynamics- Every molecule is in the spotlight in statistical thermodynamics, which means that the properties of each molecule and how they interact are taken into account to characterize the behavior of a group of molecules.
- Chemical Thermodynamics- Chemical thermodynamics deals with the study of heat and work changes during chemical reactions and phase transitions.
- Equilibrium Thermodynamics- Equilibrium thermodynamics focuses on the study of systems in equilibrium and the energy and matter changes as systems approach equilibrium.
Thermodynamic Properties
Thermodynamics deals with the bulk behavior of matter such as atoms and molecules. The macroscopic properties of a system arise from the collective behavior of a large number of particles. Thermodynamic properties are the characteristics of a system that describe its state. Thermodynamic properties are classified into two categories.
- Extensive property- Extensive properties depend on the amount or size of the substance present in the system. Their values change when the mass of the system changes. Eg: internal energy, entropy, enthalpy, free energy, volume, and mass.
- Intensive property- Intensive properties are independent of the amount or size of the substance present. Their values remain the same regardless of the system’s mass. Eg: temperature, pressure, density, viscosity, surface tension, and vapor pressure.
Thermodynamic Equilibrium
All properties of a system have fixed values at any given state. As a result, even if the value of one property changes, the system's state changes. While a system is in equilibrium, the value of its properties does not change when it is isolated from its surroundings.
- Thermal equilibrium- A system is said to be in thermal equilibrium when the temperature is the same throughout the entire system.
- Mechanical equilibrium- A system is said to be in mechanical equilibrium when there is no change in pressure at any point in the system.
- Chemical equilibrium- A chemical equilibrium is defined as a system in which the chemical composition of a system does not change over time.
- Phase equilibrium- When the mass of each phase of a two-phase system reaches an equilibrium level, it is called phase equilibrium.
If a thermodynamic system is in chemical equilibrium, mechanical equilibrium, and thermal equilibrium, and the relevant parameters cease to vary with time, then it is said to be in thermodynamic equilibrium.
Thermodynamic Process
A process can alter the state of a thermodynamic system. A process, in other words, specifies the path or procedure by which a system transitions from one state to another. The process may be accompanied by a material and energy exchange between the system and the surrounding.
When there is an energetic shift within a system that is related to changes in pressure, volume, and internal energy, it is called a thermodynamic process.
Some typical forms of thermodynamic processes have their own set of characteristics, which are listed below.
- Isothermal process-A process in which the temperature remains constant throughout. Heat is exchanged with the surroundings to maintain constant temperature.
- Adiabatic process- A process in which no heat is exchanged between the system and its surroundings. The system is thermally insulated, and the temperature usually changes during the process.
- Isobaric process- A process in which the system's pressure remains constant, i.e., no pressure change occurs.
- Isochoric process- A process in which the volume of the system remains constant, i.e., there is no change in volume and no work is done by the system.
- Reversible process- A process that can be reversed by making an infinitesimally small change in external conditions. The system remains in equilibrium with its surroundings at every stage of the process.
- Irreversible process- A process that cannot be reversed is known as irreversible. The opposing force is not the same as the driving force. Natural processes are irreversible.
- Cyclic process- A process in which the system undergoes a series of changes and eventually returns to its initial state.
Laws of Thermodynamics
Thermodynamic laws describe the fundamental principles that govern energy, temperature, entropy, and their behavior in thermodynamic systems. These laws explain how energy is transferred and transformed under different conditions. Thermodynamics is governed by four laws:
- Zeroth Law of Thermodynamics- According to the Zeroth Law of Thermodynamics, if two bodies are separately in thermal equilibrium with a third body, then the first two bodies are likewise in thermal equilibrium with each other. This indicates that if system A is in thermal equilibrium with system B, and system C is likewise in thermal equilibrium with system B, then both systems A and C are in thermal equilibrium.
- First Law of Thermodynamics-Energy can neither be created nor destroyed; it can only be transformed from one form to another. The heat supplied to a system is partly used to change its internal energy and partly to perform work.
Mathematically, it may be expressed as
ΔQ = ΔU + W
where,
- The heat given or lost is denoted by ΔQ.
- The change in internal energy is denoted by ΔU.
- W stands for work done.
The above equation can alternatively be written as follows:
ΔU = ΔQ −W
As a result of the above equation, we may deduce that the quantity (ΔQ – W) is unaffected by the path taken to change the state. Furthermore, when heat is applied to a system, internal energy tends to rise, and vice versa.
- Second Law of Thermodynamics- In an isolated system, the second law of thermodynamics asserts that in an isolated system entropy always increases with time. Natural processes occur spontaneously in the direction of maximum entropy, and the entropy of the universe never decreases.
- Third Law of Thermodynamics- As the temperature approaches absolute zero, the entropy of a system approaches a constant minimum value. For a perfect crystalline solid at absolute zero, entropy becomes zero since it has only one possible lowest energy state.
Solved Problems
Question 1: 1 mole of an ideal gas expands isothermally at 300 K from 5 L to 20 L. Calculate the change in entropy of the gas. (Given: R = 8.314 J/mol·K)
Solution:
\Delta S = nR \ln \left(\frac{V_2}{V_1}\right)
\Delta S = (1)(8.314)\ln \left(\frac{20}{5}\right)
\Delta S = 8.314 \ln (4)
\Delta S = 8.314 \times 1.386
\Delta S = 11.53 \, \text{J K}^{-1}
Question 2: 500 J of heat is supplied to a system at a constant temperature of 250 K. Find entropy change.
Solution:
\Delta S = \frac{Q}{T}
\Delta S = \frac{500}{250}
\Delta S = 2 \, \text{J K}^{-1}
Question 3: 1 kg of water at 373 K changes into steam at the same temperature. Latent heat of vaporization = 2.26 × 10⁶ J/kg. Calculate entropy change.
Solution:
\Delta S = \frac{Q}{T}
Q = mL = 1 \times 2.26 \times 10^{6}
Q = 2.26 \times 10^{6} \, \text{J}
\Delta S = \frac{2.26 \times 10^{6}}{373}
\Delta S = 6060 \, \text{J K}^{-1}
Question 4: The molar heat capacity of a solid at very low temperature varies as C = aT,3 where a = 2.5 × 10⁻³ J/K⁴·mol. Find the entropy change when temperature increases from 0 K to 5 K.
Solution:
\Delta S = \int_{0}^{T} \frac{C}{T} \, dT
\Delta S = \int_{0}^{5} \frac{aT^{3}}{T} \, dT
\Delta S = a \int_{0}^{5} T^{2} \, dT
\Delta S = a \left[ \frac{T^{3}}{3} \right]_{0}^{5}
\Delta S = 2.5 \times 10^{-3} \times \frac{125}{3}
\Delta S = 2.5 \times 10^{-3} \times 41.67
\Delta S = 0.104 \, \text{J K}^{-1}
Unsolved Problems
Question 1: Two moles of an ideal gas expand reversibly and isothermally at 300 K from 5 L to 25 L. Calculate the change in entropy of the gas.
Question 2: 0.5 kg of ice at 0°C is completely converted into water at 0°C. The latent heat of fusion of ice is 3.34 × 105⁵ J/kg. Find the change in entropy of the system.
Question 3: A substance has heat capacity C = aT2, where a = 4 × 10⁻³ J K⁻³.. It is heated from 0 K to 10 K. Calculate the total change in entropy.
Question 4: Three moles of an ideal gas undergo reversible isothermal compression at 400 K from 8 L to 2 L. Calculate the change in entropy and determine its sign.
Question 5: One kilogram of water is heated from 20°C to 100°C. The specific heat capacity of water is 4200 J/kg. K. Calculate the entropy change during the process.