CHAPTER 11- THERMODYNAMICS

• Calorie- It is a unit if energy which show the picture of heat.
• When we connect colder body to hotter body, then the calorie (fluid or heat) flow for colder body to hotter body.
• Benjamin Thomson (also known as Count Rumford) in 1798 Perform an experiment. He observed in boring of brass (lot of heat produced by drilling) that the heat is produced depend on work done not the sharpness of drill.
• Thermodynamics-
  • It is a branch of physics in which we deals with concept of heat and temperature briefly and other form form of energy.
  • It is macroscopic science.
  • It deal with bulk system, not molecular system or on microscopic level.

THERMAL EQUILIBRIUM-

• In mechanics, the equilibrium means that the net external force and torque is 0.
• But in thermodynamics, the equilibrium means if the macroscopic variable that characterise the system do not change in time.
• Some important thermodynamics terms are-
  • Adiabatic Process– The process which does not exchange heat with its surrounding. In this system have a wall which separate system or surrounding is called adiabatic wall .
  • Isothermal Process-In this process, temperature remain constant or fixed.
  • Isochoric Process– In this process, volume remain constant.
  • Isobaric Process-Change of state is brought about at constant pressure.
  • Cyclic Process-In this process, the system undergoes different changes and finally return to its initial stages.
  • Reversible Process- This process is very slow, allowing the system and surroundings to remain in equilibrium at every step, and be reversed without leaving any change in either.
  • Irreversible Process– It is real process that occur quickly, causing the system and surrounding lose equilibrium and resulting in permanent change that cannot be completely reversed.

Zero^th Law of Thermodynamics-

According to this law, the temperature is that property which determines weather two systems are in thermal equilibrium, If their temperature are equal, no heat flows between them.

Suppose 2 system A and B have separated by adiabatic wall where it both 2 connect with third system, C, which has thermal conducting wall, both come to thermal equilibrium with C. Suppose A and B have conducting wall and C has insulated from both 2 by adiabatic wall.

It state that if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

R.H. Fowler makes this law in the year 1931.

HEAT, WORK AND INTERNAL ENERGY-

Heat, Internal Energy, and Work

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Basic Concepts

1. Temperature & Zeroth Law of Thermodynamics:
   • Temperature: Measures how “hot” or “cold” an object is. It dictates the direction of heat flow between two objects in thermal contact.
   • Thermal Equilibrium: Heat flows from a hotter body to a colder one until their temperatures are equal.
   • Zeroth Law: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This defines temperature as a measurable quantity.

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Internal Energy (U):

• Every system is made of molecules with kinetic energy (due to motion) and potential energy (due to interactions).
• Internal Energy: The total of all molecular energies (kinetic + potential) in the system, excluding the motion of the system as a whole.
• Internal energy is a state variable, meaning it depends only on the current state (pressure, volume, temperature) of the system, not on how the state was achieved.

Key Points:

• For gases, internal energy is mostly the kinetic energy of randomly moving molecules.
• Internal energy changes due to heat transfer or work done on/by the system.

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Work (W) and Heat (Q):

• Both are modes of energy transfer that alter internal energy.
• Heat: Energy transfer due to a temperature difference between system and surroundings.
• Work: Energy transfer caused by macroscopic forces (e.g., moving a piston in a cylinder).

Distinction:

• Internal Energy (U): A property of the system (state variable).
• Heat (Q) & Work (W): Processes; they describe energy in transit and depend on the path taken.

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Changing Internal Energy:

• To increase internal energy:
  1. Add Heat (Q): Place the system in contact with something hotter.
  2. Do Work (W): Compress the system (e.g., push a piston).
• To decrease internal energy:
  1. Lose Heat (Q): Place the system in contact with something cooler.
  2. Let System Do Work (W): Expand the system (e.g., gas pushes a piston outward).

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First Law of Thermodynamics:

• States energy conservation for thermodynamic systems:ΔQ=ΔU+ΔW\Delta Q= ΔU+ΔW
  • ΔQ: Heat supplied to the system.
  • ΔW: Work done by the system on surroundings.
  • ΔU: Change in internal energy.
• Rearranged form:ΔU= ΔQ−ΔW

Implications:

• The energy supplied to a system (heat/work) increases internal energy or does work.
• In isothermal processes (constant temperature), internal energy remains unchanged (ΔU=0), so ΔQ= ΔW.

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Heat Capacity:

• Heat Capacity (S): Amount of heat required to raise a substance’s temperature.
  • S=ΔQ/ΔT
• Specific Heat Capacity (s): Heat capacity per unit mass.
  • s=S/m =ΔQ/mΔT​
  • Unit: J kg⁻¹ K⁻¹J
• Molar Heat Capacity (C): Heat capacity per mole of substance.
  • C=ΔQ/μΔT
  • Unit: J mol⁻¹ K⁻¹J
• Water’s specific heat: 4186 J kg⁻¹ K⁻¹ (important for heat transfer calculations).

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Work Done by Gases:

• For a gas at constant pressure: ΔW=PΔV
• Heat added (ΔQ) splits into:
  • Increasing internal energy (ΔU).
  • Doing work (PΔV).

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Specific Heat in Gases:

• Two types for gases:
  1. C_v​: Heat capacity at constant volume (ΔV=0).
  2. Cp​: Heat capacity at constant pressure.
• Relation: C_p – C_v= R
  • R: Universal gas constant (8.314 J mol⁻¹ K⁻¹).

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State Variables and Equilibrium:

• State Variables: Properties that define a system’s state (e.g., pressure, volume, temperature, internal energy).
  • Extensive: Depend on system size (e.g., volume, mass).
  • Intensive: Independent of size (e.g., pressure, temperature).
• Equation of State: Relates state variables (e.g., Ideal Gas Law: PV=nRT).

Extra Tip for Competitive Exams:

• Remember key thermodynamic processes:
  • Isothermal: ΔU=0
  • Adiabatic: ΔQ=0
  • Isochoric: ΔW=0
  • Isobaric: P=constant

Thermodynamic Processes

• Thermodynamics studies energy transfer and its effects on matter. Thermodynamic processes involve changes in a system’s pressure, volume, temperature, or heat.

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Quasi-static Process

• Definition: A process where the system remains in equilibrium throughout. Changes occur very slowly, keeping the system in thermal and mechanical equilibrium with its surroundings.
• Key Points:
  • Pressure and temperature differences between the system and surroundings are infinitesimal.
  • Idealized and infinitely slow, approximated in real-world slow processes without abrupt changes.
  • Examples: Gradual expansion or compression of gas.

Special Thermodynamic Processes

Process Type	Property Held Constant	Key Formula/Insights
Isothermal	Temperature (T)	PV=constant, follows Boyle’s Law. Work W=μRTln⁡(V2/V1).
Adiabatic	No heat transfer (Q=0)	PVγ= constant, γ=Cp/Cv
Isochoric	Volume (V)	No work done, heat changes internal energy.
Isobaric	Pressure (P)	Work W=P(V2​−V1​). ​
Cyclic	Returns to initial state	ΔU=0, heat absorbed equals work done.

Isothermal Process

• Key Idea: Temperature remains constant.
• Work Done:W=μRT ln (V₂/V₁)
• Important:
  • For expansion (V₂>V_1​), work is done by the gas, and it absorbs heat.
  • For compression (V₂<V₁​), work is done on the gas, and heat is released.

Adiabatic Process

• Key Idea: No heat exchange. Work done changes internal energy.
• Equation: PV^γ=constant.
• Important:
  • Work done causes temperature to drop (expansion) or rise (compression).
  • Work W= (P₁V₁−P₂V₂) / (γ−1)

Isochoric Process

• Key Idea: Volume constant, no work is done.
• Heat Transfer: Directly changes the system’s internal energy (Q=ΔU).

Isobaric Process

• Key Idea: Pressure constant.
• Work Done: W= μR(T₂​−T₁​)
• Heat Transfer: Splits between increasing internal energy and doing work.

Cyclic Process

• Key Idea: System returns to its initial state.
• Result: Total internal energy change ΔU=0. Heat absorbed equals work done.

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Second Law of Thermodynamics

• Statement:
  1. Kelvin-Planck: No engine can convert all heat absorbed into work.
  2. Clausius: Heat cannot flow spontaneously from colder to hotter body.
• Implications:
  • Perfect efficiency in heat engines or infinite performance in refrigerators is impossible.
  • Defines the direction of natural processes and irreversibility.

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Reversible vs. Irreversible Processes

• Reversible: Hypothetical, ideal processes with no dissipative effects. Achieved through quasi-static changes.
  • E.g., Slow isothermal expansion in a frictionless piston.
  • Significance: Provides maximum efficiency limits for engines.
• Irreversible: Real-world processes with friction, heat gradients, or rapid changes.
  • E.g., Free expansion of gas, diffusion, combustion.

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Competitive Exam Insights

1. Efficiency of Heat Engines:
   • Max efficiency η= 1−T₂​/T_1​ for a reversible engine (Carnot engine).
   • Real engines always have lower efficiency due to irreversibility.
2. Work Relations:
   • Use ideal gas laws and process-specific equations to calculate work and heat.
3. Second Law Applications:
   • Analyze entropy changes and feasibility of processes.
4. Graphical Analysis:
   • Interpret P−V and T−S curves for different processes.

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Common Question Types

• Numerical Problems:
  • Calculate work done, heat transfer, or efficiency using process equations.
• Conceptual Questions:
  • Identify processes from given conditions (e.g., constant temperature → isothermal).
• Graph Analysis:
  • Interpret shifts in P−V or T−S diagrams.
• Real-Life Examples:
  • Discuss irreversibility in practical systems like engines, refrigerators.

1. Basics of the Carnot Engine:

• A Carnot engine is an ideal, reversible heat engine that works between two temperatures:
  • Hot reservoir temperature (T₁): High temperature.
  • Cold reservoir temperature (T₂): Low temperature.
• Goal: Determine the maximum possible efficiency and the processes required for this efficiency.

2. Key Processes in the Carnot Cycle:

The Carnot cycle consists of four steps, alternating between isothermal and adiabatic processes:

1. Isothermal Expansion (T₁):
   • Gas absorbs heat (Q₁) from the hot reservoir at constant temperature T₁.
   • Work W₁ → ₂ is done by the gas.
   • Work formula: W₁→₂=Q₁=μRT₁ln (V₂ / V₁)
2. Adiabatic Expansion (T₁ → T₂):
   • Gas expands without exchanging heat; its temperature drops from T₁ to T₂.
   • Work formula: W₂​→₃​= μR(T₁​−T₂​)​ / γ−1
3. Isothermal Compression (T₂):
   • Gas releases heat (Q₂) to the cold reservoir at constant temperature T₂.
   • Work W₃ → ₄ is done on the gas.
   • Work formula: W₃​→₄​= Q₂​= μRT₂​ln (V₃​/V₂​)
4. Adiabatic Compression (T₂ → T₁):
   • Gas is compressed without exchanging heat, returning to its initial temperature T₁.
   • Work formula:W₄​→₁​= μR (T₁​−T₂​)​/(γ−1)​

3. Efficiency of the Carnot Engine:

• Efficiency (η\etaη) measures how effectively the engine converts heat into work.
• Formula: η= 1− (​T_2​​/ T₁)
  • Efficiency depends only on the temperatures of the reservoirs.
  • Higher T₁​ or lower T₂​ increases efficiency.

4. Key Features of the Carnot Engine:

• Reversibility: All processes are ideal and quasi-static (very slow to avoid dissipative effects).
• Maximum Efficiency: No real engine can be more efficient than a Carnot engine between the same temperatures.
• Universality: Efficiency is independent of the working substance (e.g., gas, liquid).

Important Theoretical Insights:

1. Carnot’s Theorem:
   • No engine working between two given temperatures can surpass the efficiency of a Carnot engine.
2. Thermodynamic Temperature Scale:
   • Relation: Q₂/Q₁ = T₂/T₁​​
   • This relation defines a universal temperature scale.

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Additional Knowledge to Solve Questions:

Thermodynamic Laws Related to Carnot Engine:

1. First Law of Thermodynamics:ΔQ=ΔU+ΔW
   • Heat added (Q) equals the change in internal energy (U) plus the work done (W).
2. Second Law of Thermodynamics:
   • Heat cannot fully convert into work without some being released to a cold reservoir.
   • Implies η < 1.

Key Formulas to Remember:

1. For Isothermal Processes: Q= W= μRTln (​V_f/V_i​​)
2. For Adiabatic Processes: PV^γ= constant, W= μR(T₁​−T₂​)​/(γ−1)

Efficiency Improvement Tips:

• Increase T₁: Use a higher temperature source.
• Decrease T₂​: Lower the sink temperature, but practical limits exist (absolute zero is unattainable).

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Concepts for Competitive Exams:

1. Real vs. Ideal Engines:
   • Real engines face losses due to friction, heat dissipation, etc., making their efficiency lower than Carnot engines.
2. Applications of the Carnot Cycle:
   • Helps understand practical engines, like steam engines and refrigeration systems.
3. Refrigeration Principle:
   • Reversing the Carnot cycle makes it act as a refrigerator, absorbing heat from a cold reservoir and releasing it to a hot reservoir.

These all are the notes of chapter 11 in physics. And after some time you get important questions and NCERT solutions HERE. *#THANKS FOR VISITING, VISIT AGAIN#* 😊