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Class 11 Science (PCM)

Physics Part 2

Thermodynamics

Thermodynamics

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Study Action Plan (Sorted by Difficulty)
Adiabatic Process
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Carnot Cycle and Efficiency
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First Law of Thermodynamics
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Heat Engines and Refrigerators
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Heat, Internal Energy and Work
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Isobaric, Isochoric and Cyclic Processes
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Isothermal Process
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Reversible and Irreversible Processes
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Second Law of Thermodynamics
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Specific Heat Capacity
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Thermal Equilibrium and Thermodynamic System
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Thermodynamic State Variables
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Work Done by Gas and P–V Diagram
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Zeroth Law of Thermodynamics
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Learning Objectives

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Learning Objectives

  • Understand the principle of conservation of energy as applied to thermodynamic systems through the First Law of Thermodynamics, expressed as Q=ΔU+WQ = \Delta U + W.
  • Analyze the limitations imposed by the Second Law of Thermodynamics on the efficiency of heat engines and the performance of refrigerators.
  • Calculate the efficiency of a Carnot cycle, the most efficient reversible cycle possible between two heat reservoirs, using the formula η=1−T2T1\eta = 1 - \frac{T_2}{T_1}.
  • Apply the Zeroth Law of Thermodynamics to understand the concept of temperature and thermal equilibrium.
  • Solve problems involving adiabatic processes, characterized by the relation PVγ=constantPV^\gamma = \text{constant} for an ideal gas, where γ\gamma is the heat capacity ratio.
  • Evaluate isothermal processes where temperature remains constant, and the product of pressure and volume is constant (PV=constantPV = \text{constant}).
  • Identify thermodynamic state variables such as pressure, volume, temperature, and internal energy, and understand their role in describing the equilibrium state of a system.
  • Calculate specific heat capacity and understand its significance in relation to the amount of heat required to change the temperature of a substance.
  • Distinguish between reversible and irreversible processes, recognizing that reversible processes are idealized and can be reversed without leaving any change in both the system and surroundings.
  • Explore the concept of thermal equilibrium and the interaction between thermodynamic systems through adiabatic and diathermic walls.
  • Differentiate between heat, internal energy, and work as modes of energy transfer, and understand their implications in thermodynamic processes.
  • Analyze work done by gas in expansion and compression using P-V diagrams, and understand the path dependence of work.
  • Investigate isobaric, isochoric, and cyclic processes, and calculate changes in work, heat, and internal energy for each case.
  • Examine the efficiency of heat engines and refrigerators, and the limitations imposed by the Second Law of Thermodynamics on their performance.

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Revision Notes & Summary

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Chapter Notes

First Law of Thermodynamics

  • Definition: The principle of conservation of energy applied to thermodynamic systems.
  • Formula: Q=ΔU+WQ = \Delta U + W
    • QQ: Heat supplied to the system
    • ΔU\Delta U: Change in internal energy
    • WW: Work done by the system
  • Key Points:
    • Heat and work are modes of energy transfer.
    • Internal energy depends only on the state of the system, not on how it was achieved.

Second Law of Thermodynamics

  • Definition: No process is possible whose sole result is the absorption of heat from a reservoir and complete conversion into work.
  • Kelvin-Planck Statement: No process can convert all absorbed heat into work.
  • Clausius Statement: Heat cannot spontaneously flow from a colder body to a hotter body.
  • Implications:
    • Efficiency of a heat engine can never be 100%.
    • Coefficient of performance for refrigerators cannot be infinite.

Carnot Cycle and Efficiency

  • Carnot Cycle: The most efficient reversible cycle possible between two heat reservoirs.
  • Efficiency Formula: η=1−T2T1\eta = 1 - \frac{T_2}{T_1}
    • T1T_1: Temperature of the hot reservoir
    • T2T_2: Temperature of the cold reservoir
  • Key Points:
    • Carnot cycle consists of two isothermal and two adiabatic processes.
    • Represents the maximum efficiency achievable.

Zeroth Law of Thermodynamics

  • Definition: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
  • Concept: Leads to the definition of temperature.

Adiabatic Process

  • Definition: A process with no heat exchange with the surroundings.
  • Relation: PVγ=constantPV^\gamma = \text{constant} for an ideal gas.
    • γ\gamma: Heat capacity ratio (Cp/CvC_p/C_v)

Isothermal Process

  • Definition: A process in which the temperature remains constant.
  • Relation: For an ideal gas, PV=constantPV = \text{constant}.

Thermodynamic State Variables

  • Examples: Pressure, volume, temperature, internal energy.
  • Characteristics: Independent of the path taken to reach that state.

Specific Heat Capacity

  • Definition: Heat required to change the temperature of a unit mass of a substance by one degree.
  • Formula: C=QmΔTC = \frac{Q}{m \Delta T}
    • CpC_p: Specific heat at constant pressure
    • CvC_v: Specific heat at constant volume

Reversible and Irreversible Processes

  • Reversible: Idealized processes that can be reversed without leaving any change in both the system and surroundings.
  • Irreversible: Natural processes that cannot be reversed.

Thermal Equilibrium and Thermodynamic System

  • Thermal Equilibrium: No net heat flow between systems in contact.
  • System-Surroundings Interaction: Defined by adiabatic or diathermic walls.

Heat, Internal Energy and Work

  • Heat: Energy transfer due to temperature difference.
  • Internal Energy: Sum of kinetic and potential energies of molecules.
  • Work: Energy transfer by means other than heat.

Work Done by Gas and P–V Diagram

  • Formula: ΔW=PΔV\Delta W = P\Delta V
  • P-V Diagram: Area under the curve represents work done.

Isobaric, Isochoric and Cyclic Processes

  • Isobaric: Constant pressure
  • Isochoric: Constant volume
  • Cyclic: Returns to initial state, ΔU=0\Delta U = 0

Heat Engines and Refrigerators

  • Heat Engine Efficiency: Cannot be 100% due to the Second Law.
  • Coefficient of Performance: Measure of efficiency for refrigerators and heat pumps.
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Practice Test – MCQs, True/False

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Multiple Choice Questions

A.

In thermal equilibrium, the temperatures of two systems are equal.

B.

Thermal equilibrium implies that no heat can flow between two systems.

C.

Thermal equilibrium can only occur if both systems are in mechanical equilibrium.

D.

Thermal equilibrium requires that both systems have the same pressure.
Correct Answer: A

Solution:

Thermal equilibrium is defined as the state where two systems in contact with each other do not exchange heat, which occurs when their temperatures are equal.

Chapter Concept:

Thermal Equilibrium and Thermodynamic System

A.

The work done is positive.

B.

The work done is negative.

C.

The work done is zero.

D.

The work done depends on the temperature change.
Correct Answer: C

Solution:

In an isochoric process, the volume remains constant, so no work is done by the gas.

Chapter Concept:

Isobaric, Isochoric and Cyclic Processes

A.

The temperature increases.

B.

The temperature decreases.

C.

The temperature remains constant.

D.

The temperature change is unpredictable.
Correct Answer: B

Solution:

In an adiabatic expansion, the gas does work on the surroundings, which results in a decrease in its internal energy and hence a decrease in temperature.

Chapter Concept:

Adiabatic Process

A.

It states that the total energy of an isolated system is constant.

B.

It states that energy can be created or destroyed in an isolated system.

C.

It states that the efficiency of a heat engine can be 100%.

D.

It states that the entropy of an isolated system always decreases.
Correct Answer: A

Solution:

The First Law of Thermodynamics is the principle of conservation of energy, stating that the total energy of an isolated system is constant.

Chapter Concept:

First Law of Thermodynamics

A.

63.1 kPa

B.

71.2 kPa

C.

80.0 kPa

D.

90.0 kPa
Correct Answer: A

Solution:

For an adiabatic process, P1V1γ=P2V2γP_1 V_1^\gamma = P_2 V_2^\gamma. Substituting the given values: 100×11.4=P2×21.4100 \times 1^{1.4} = P_2 \times 2^{1.4}. Solving for P2P_2, we get P2=10021.4≈63.1 kPaP_2 = \frac{100}{2^{1.4}} \approx 63.1 \text{ kPa}.

Chapter Concept:

Specific Heat Capacity

A.

1−T2T11 - \frac{T_2}{T_1}

B.

T2T1\frac{T_2}{T_1}

C.

1+T2T11 + \frac{T_2}{T_1}

D.

T1T2\frac{T_1}{T_2}
Correct Answer: A

Solution:

The efficiency of a Carnot engine is given by 1−T2T11 - \frac{T_2}{T_1}, where T1T_1 is the temperature of the hot reservoir and T2T_2 is the temperature of the cold reservoir.

Chapter Concept:

Isothermal Process

A.

Heat is absorbed by the system.

B.

No heat is exchanged with the surroundings.

C.

The process is always isothermal.

D.

The system is in thermal equilibrium with the surroundings.
Correct Answer: B

Solution:

In an adiabatic process, the system is insulated from the surroundings and no heat is exchanged.

Chapter Concept:

Reversible and Irreversible Processes

A.

The area under the P-V curve

B.

The slope of the P-V curve

C.

The intercept of the P-V curve

D.

The area above the P-V curve
Correct Answer: A

Solution:

The work done by a gas during expansion is represented by the area under the P-V curve.

Chapter Concept:

Work Done by Gas and P–V Diagram

A.

A reversible process can be reversed without leaving any change in both the system and surroundings.

B.

A reversible process is a natural process that cannot be reversed.

C.

A reversible process always involves a change in the state variables.

D.

A reversible process is characterized by a rapid change in temperature.
Correct Answer: A

Solution:

A reversible process is idealized and can be reversed without leaving any change in both the system and surroundings.

Chapter Concept:

Reversible and Irreversible Processes

A.

Energy can neither be created nor destroyed.

B.

No process is possible whose sole result is the absorption of heat from a reservoir and complete conversion into work.

C.

The internal energy of a system is the sum of kinetic and potential energies of its molecules.

D.

The temperature of a body is related to its average internal energy.
Correct Answer: B

Solution:

The Second Law of Thermodynamics states that no process is possible whose sole result is the absorption of heat from a reservoir and complete conversion into work, as per the Kelvin-Planck statement.

Chapter Concept:

Second Law of Thermodynamics

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True or False

Correct Answer: True

Solution:

Reversible processes are idealized processes that can be reversed without leaving any change in both the system and surroundings, as stated in the text.

Chapter Concept :

Reversible and Irreversible Processes

Correct Answer: True

Solution:

In an isothermal process, the temperature of the system remains constant. For an ideal gas, the internal energy is a function of temperature only. Therefore, if the temperature does not change, the internal energy remains constant.

Chapter Concept :

Isothermal Process

Correct Answer: False

Solution:

Heat and work are not state variables. They are modes of energy transfer that result in changes to the internal energy of a system, which is a state variable.

Chapter Concept :

Heat, Internal Energy and Work

Correct Answer: True

Solution:

In an adiabatic process, no heat is exchanged with the surroundings, and for an ideal gas, the relation PVγ=constantPV^\gamma = \text{constant} is valid, where γ\gamma is the ratio of specific heats at constant pressure and volume.

Chapter Concept :

Adiabatic Process

Correct Answer: True

Solution:

In thermodynamics, the work done by a gas during expansion or compression is dependent on the path taken in the P-V diagram, as the area under the curve represents the work done.

Chapter Concept :

Work Done by Gas and P–V Diagram

Correct Answer: True

Solution:

Thermodynamic state variables describe the equilibrium state of a system and are independent of the path taken to reach that state. This is a fundamental property of state variables.

Chapter Concept :

Thermodynamic State Variables

Correct Answer: True

Solution:

The work done by a gas in a thermodynamic process depends on the path taken from the initial to the final state. In contrast, the change in internal energy depends only on the initial and final states, not on the path taken.

Chapter Concept :

Work Done by Gas and P–V Diagram

Correct Answer: True

Solution:

The Zeroth Law of Thermodynamics establishes the concept of temperature by stating that if two systems are in thermal equilibrium with a third system, they must be in thermal equilibrium with each other.

Chapter Concept :

Zeroth Law of Thermodynamics

Correct Answer: False

Solution:

According to the Second Law of Thermodynamics, no process is possible whose sole result is the absorption of heat from a reservoir and complete conversion into work.

Chapter Concept :

Second Law of Thermodynamics

Correct Answer: True

Solution:

For an ideal gas, internal energy depends only on temperature. In an isothermal process, the temperature remains constant, hence the change in internal energy is zero.

Chapter Concept :

First Law of Thermodynamics

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