Revision: 12th Std >> Thermodynamics MAH-MHT CET (PCM/PCB) Thermodynamics

A part of the universe chosen for analysis, separated by boundaries, where energy and matter exchanges are observed, is called a thermodynamic system.

OR

An assembly of an extremely large number of particles (atoms or molecules) in solid, liquid, gaseous, or a combination of two or more phases is called a thermodynamic system.

The branch of science which deals with exchange of heat energy between bodies and conversion of heat energy into mechanical energy and vice versa is called thermodynamics.

A system that exchanges both energy and matter with its surroundings is called an open system.

Everything outside the system which has direct effect on the system is called its surrounding.

A system that exchanges neither energy nor matter with its surroundings is called an isolated system.

A system that exchanges only energy (not matter) with its surroundings is called a closed system.

The state of a system in which its properties do not change as long as external conditions remain unchanged is called the thermodynamic equilibrium state.

• It satisfies: mechanical equilibrium (no unbalanced forces), thermal equilibrium (no temperature differences), and chemical equilibrium (no reaction).

The state in which two objects are at the same temperature and there is no net flow of heat between them is called thermal equilibrium.

The energy transfer due to temperature difference between a system and its surroundings is called heat.

OR

The energy that exchanges between a system and its environment because of the temperature difference between them is called heat.

• SI unit: joule (J); CGS unit: calorie

The energy transferred to or from a system when an external force acts on the system's boundary, causing it to move, is called work.

The total energy possessed by any system due to molecular motion and molecular configuration is called internal energy.

OR

The energy possessed by a system due to molecular motion and molecular configuration is called internal energy.

where U_k​ = internal kinetic energy (due to molecular motion) and U_p​ = internal potential energy (due to molecular configuration).

One calorie is defined as the amount of heat energy needed to raise the temperature of one gram of water by one degree Celsius at a pressure of one atmosphere.

The internal energy of a thermodynamic system is the sum of kinetic and potential energies of all the molecules of the system with respect to the center of mass of the system.

A quasi-static process is an infinitely slow process in which the system changes its variables (P, V, T) so slowly such that it remains in thermal, mechanical, and chemical equilibrium with its surroundings throughout.

The total internal energy of all the molecules of a substance is called its thermal energy.

The measurement of the quantity of heat is called calorimetry.

Heat is that form of energy which flows from a hot body to a cold body when they are kept in contact.

The kinetic energy due to random motion of the molecules of a substance is known as its heat energy.

One kilo-calorie of heat is the heat energy required to raise the temperature of 1 kg of water from 14.5°C to 15.5°C.

The sum of the potential energy and kinetic energy of a molecule is called its internal energy.

The specific values of macroscopic variables that completely describe every equilibrium state of a thermodynamic system are called thermodynamic state variables.

The thermodynamic state variables that depend on the size of the system (e.g., internal energy, volume) are called extensive variables.

The thermodynamic state variables that do not depend on the size of the system (e.g., pressure, temperature) are called intensive variables.

The state of a system in which the three conditions — mechanical equilibrium, chemical equilibrium, and thermal equilibrium — are satisfied simultaneously is called thermodynamic equilibrium.

An idealised process in which at every stage the system is in equilibrium state (very slow process) is called a quasi-static process.

A procedure by which the initial state of a system changes to the final state is called a thermodynamic process.

A process in which the changes can be retraced in the reverse direction (e.g., melting of ice, freezing of water, condensation of steam) is called a reversible process.

The thermodynamic quantity that combines internal energy with the pressure-volume product, defined as H = U + PV, is called enthalpy.

A process in which the changes cannot be retraced in the reverse direction (e.g., puncturing an inflated balloon, burning a candle) is called an irreversible process.

A process in which the temperature of the system is kept constant during the change in state (T = constant) is called an isothermal process.

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A thermodynamic process that takes place at constant temperature in which the internal energy of a system remains unchanged (ΔT = 0, ΔU  =0) is called an isothermal process.

A process in which the pressure is kept constant (pp = constant) is called an isobaric process.

OR

A thermodynamic process in which the pressure of the system remains constant (ΔP = 0=) is called an isobaric process.

A process in which the volume is kept constant (V = constant) is called an isochoric process.

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A thermodynamic process in which the volume of the system remains constant (ΔV = 0) is called an isochoric process.

A process in which there is no exchange of heat between the system and its surroundings, and the system is perfectly insulated from its environment, is called an adiabatic process.

OR

The process during which the heat content of the system or certain quantity of the matter remains constant, i.e., there is no transfer of heat between the system and its surroundings (ΔQ = 0), is called an adiabatic process.

A process in which the system returns to its initial state is called a cyclic process.

An adiabatic expansion in which there is no exchange of heat between a system and its surroundings is called free expansion.

A device that transforms heat partly into work or mechanical energy (where T_H > T_C​, Q_H > 0, Q_C < 0) is called a heat engine.

Heat engine is a device which takes heat as input and converts this heat into work by undergoing a cyclic process.

A device that converts heat into work, where some heat is always lost as waste heat, with its performance measured by efficiency, is called a heat engine.

A device that extracts heat from a cold region and delivers it to the surroundings, further cooling the cold region (where QC > 0, QH < 0, W < 0) is called a refrigerator.

OR

A system that requires external work to transfer heat from a lower temperature to a higher temperature, with its performance measured by the Coefficient of Performance (COP), is called refrigeration.

It is defined as the ratio of heat extracted from the cold body (sink) to the external work done by the compressor W.

A device that cools indoor spaces by removing heat from inside and releasing it outside, with its performance measured by COP, is called an air conditioner.

A device that works similar to a refrigerator but is used to heat a building or a similar larger structure, with its performance measured by COP, is called a heat pump.

A useful state variable that measures the change in heat divided by the temperature of the system, where the combined entropy of the system and its environment remains constant if the process approaches reversibility, is called entropy.

An ideal heat engine that operates on the Carnot cycle between a hot reservoir (T_H​) and a cold reservoir (T_C​) to give maximum possible efficiency is called a Carnot engine.

An ideal thermodynamic cycle that provides maximum possible efficiency operating between two temperature limits, consisting of four reversible processes, is called the Carnot cycle.

A thermodynamic cycle known for its high efficiency, consisting of four processes — isothermal expansion, isochoric heat removal, isothermal compression, and isochoric heat addition — is called the Sterling cycle.

ΔU = \[\frac {3}{2}\]​nRΔT

ΔQ = ms(T₂​ − T₁​)

By substituting equation W = −p_ex . ΔV in the equation ΔU = q + W, we get

ΔU = q − p_ex . ΔV  ...(1)

If the reaction is carried out in a closed container so that the volume of the system is constant, then Δ = 0. In such a case, no work is involved.

The equation (1) becomes ΔU = q_v

Equation (1) suggests that the change in internal energy of the system is due to heat transfer. The subscript v indicates a constant volume process. As U is a state function, qv is also a state function. We see that an increase in the internal energy of a system is numerically equal to the heat absorbed by the system in a constant volume (isochoric) process.

Free Expansion is a special case where:

• Q = 0 → No heat is exchanged with the surroundings (adiabatic)
• W = 0 → No work is done by or on the system
• ΔU = 0 → There is no change in internal energy of the system

\[\eta=\frac{\text{Work output}}{\mathrm{Heat~input}}\times100\%\]

COP = \[\frac {\text {Heat removed from cold reservoir​}}{\text {Work input}}\]

COP = \[\frac {\text {Heat removed from indoor space​}}{\text {Work input}}\]

COP = \[\frac {\text {Heat delivered to hot reservoir}}{\text {Work input}}\]

ΔS = \[\frac {ΔQ}{T}\]

Statement: According to the Zeroth Law, when system A and B are in thermal equilibrium, and B and C are also in thermal equilibrium, then A and C will also be in thermal equilibrium.

• The Zeroth Law leads to the concept of temperature (T).
• Thermal equilibrium means when two bodies are brought into contact, separated by a barrier permeable to heat, there will be no transfer of heat from one to the other.
• This law defines temperature and makes thermometers possible to be made.
• For thermometers to be useful, they must first be calibrated.
• All three objects (A, B, C) at thermal equilibrium are at the same temperature — this forms the basis for comparison of temperatures.

By substituting equation W = −p_ex . ΔV in the equation ΔU = q + W, we get

ΔU = q − p_ex . ΔV  ...(1)

If the reaction is carried out in a closed container so that the volume of the system is constant, then Δ = 0. In such a case, no work is involved.

The equation (1) becomes ΔU = q_v

Equation (1) suggests that the change in internal energy of the system is due to heat transfer. The subscript v indicates a constant volume process. As U is a state function, qv is also a state function. We see that an increase in the internal energy of a system is numerically equal to the heat absorbed by the system in a constant volume (isochoric) process.

Statement:
The net heat energy supplied to a system is equal to the sum of the change in internal energy of the system and the work done by the system. It is based on the law of conservation of energy.

Formula:

where Q = heat added, ΔU = change in internal energy, W = work done by the system.

Kelvin-Planck Statement: It is not feasible for any heat engine to utilise all the heat it receives from a source and convert it entirely into useful work. In other words, achieving 100% efficiency in converting heat into work is impossible.

Clausius Statement: Without any external assistance, a machine cannot transfer heat from a colder reservoir to a hotter one. In essence, heat cannot spontaneously move from a cooler object to a warmer one without external intervention or work being done.

The second law of thermodynamics states that the total entropy of a system and its surroundings increases in a spontaneous process.

Mathematically,

ΔS_total = `Delta S_"system" + Delta S_"surroundings" gt 0`

For an equilibrium:

ΔS_total = 0

• Isothermal → P-V diagram: Hyperbolic curve (inverse relation); T-V: horizontal line; T-P: vertical line.
• Adiabatic → P-V diagram: Steeper curve than isothermal; T-V: exponential decay/growth; P-T: exponential decay/growth.
• Work done = area under the P-V curve.
• Adiabatic curve is steeper because γ > 1 (slope = −γP/V vs −P/V for isothermal).

Every system is associated with a definite amount of energy stored in it, called its internal energy (U). It is the sum of all forms of kinetic and potential energies of the particles in the system.

• Internal energy is a state function — its change depends only on initial and final states.
• It is an extensive property.

Internal energy changes when:

• Heat flows into or out of the system
• Work is done on or by the system
• Matter enters or leaves the system

• Heat is the energy that flows from a hot body to a cold body when they are kept in contact.
• The S.I. unit of heat is joule (J), while calorie and kilocalorie are commonly used units.
• One calorie is approximately equal to 4.2 joule, and kilocalorie is used to measure the energy value of foods.

• Every substance possesses a definite amount of energy.
• This energy stored within a substance is called internal energy (U).
• Internal energy is the sum of kinetic energy and potential energy of all the particles in the system.
• Change in internal energy is given by:
  ΔU = U₂ − U₁

First Law: Energy of system + surroundings remains constant → ΔU = q + W

ΔU: change in internal energy, q: heat, W: work done on system

Sign convention:

• Work by system (−)
• on system (+)
• Heat absorbed (+)
• released (−)

ΔU > 0: energy enters system; ΔU < 0: energy leaves system

• Isothermal: ΔU = 0 → q = −W
• Adiabatic: q = 0 → ΔU = W
• Isochoric: W = 0 → ΔU = q
• Isobaric: ΔU = q + W

A system is in thermodynamic equilibrium if the following three conditions are satisfied simultaneously:

Reversible vs. Irreversible Processes:

• The Second Law states that there exists a useful state variable called entropy S.
• If a system's change in entropy ΔS = ΔQ/T, the combined entropy of the system and environment remains constant if the process is reversible.
• The Second Law shows: if a physical process is irreversible, the combined entropy of the system and environment increases.
• Final entropy must be greater than initial entropy for an irreversible process: S_f > S_i
• For any process approaching reversibility: ΔS_total ≥ 0
• For an isolated system: ΔU_system ≥ 0 and ΔS_total ≥ 0
• The Second Law is also known as the Law of Increased Entropy.
• No process is possible whose sole result is the absorption of heat from a reservoir and conversion of that heat entirely into work (Kelvin-Planck statement).

Entropy (S): A thermodynamic property that measures the degree of randomness or disorder of a system.

\[\Delta S=\frac{q_{rev}}{T}\]

Second Law: The entropy of the universe always tends to increase during any spontaneous process.

Total entropy change:

Entropy of mixing:

(ΔS for mixing is always positive, since ΔS is always fractional/positive)

• The Carnot cycle is an ideal thermodynamic cycle.
• It provides maximum possible efficiency between two temperature limits T_H and T_C​.
• All four processes are reversible.
• Q_H​ = heat absorbed at hot reservoir; Q_C​ = heat rejected at cold reservoir.

• The Sterling cycle uses regeneration (processes 2→3 and 4→1), which makes it highly efficient.
• Q_H​ = heat absorbed during isothermal expansion (at hot end)
• Q_C​ = heat rejected during isothermal compression (at cold end)
• No formulas are given in the provided content beyond the process descriptions.