Thermodynamics
CLASS XII PHYSICS - NEB CURRICULUM
Introduction
Thermodynamics is the branch of physics that deals with the concepts of heat,
temperature, and the inter-conversion of heat and other forms of energy.
❖ It is a macroscopic science.
❖ it deals with bulk systems and does not go into the molecular constitution of
matter.
The term comes from Greek: therme (heat) and dynamis (power).
Examples
Automobiles
Refrigeration
Internal combustion engines in
cars and bikes operate on
thermodynamic cycles,
converting heat energy from fuel
into mechanical work.
Refrigerators and air
conditioners use
thermodynamic principles to
remove heat from a colder
body and reject it to a hotter
surroundings.
Power Plants
Thermal and nuclear power
plants rely on the laws of
thermodynamics to
efficiently generate
electricity from raw thermal
energy.
Thermodynamical Universe
System, Boundary, and Surroundings
Thermodynamic Universe
System: A specific portion of the universe
chosen for thermodynamic study
or
investigation (e.g., gas in a cylinder).
Surroundings: Everything outside the system that can interact with it and affect its
behavior.
Boundary: The real or imaginary surface that separates the system from its surroundings. It
may be real or imaginary, diathermic, adiabatic, rigid and movable.
Universe: The combination of the system and its surroundings. (Universe = System +
Surroundings).
Classification of Systems
Thermodynamic systems are classified based on the permitted exchange of mass and energy across their
boundaries.
Open System
Exchanges both Mass and
Energy with surroundings.
Isolated System
Exchanges Neither Mass
nor Energy with
surroundings.
Closed System
Exchanges Energy but NOT
Mass with surroundings.
Open System
In an open system, the boundary allows the
transfer of both mass and energy (heat and work)
to and from the surroundings.
Example: An open pot of boiling water on a stove.
❖ Energy exchange: Heat is supplied by the stove, and
heat escapes into the surrounding
air.
❖ Mass exchange: Water vapor (steam) leaves the pot
and enters the atmosphere, reducing
the mass of the system.
Closed System
In a closed system, the boundary allows the transfer of energy (heat and
work) but strictly prohibits the transfer of mass.
Example: A sealed pressure cooker on a stove.
❖ Energy exchange: Heat from the stove enters the cooker,
increasing the internal energy.
❖ No Mass exchange: The lid is sealed tightly; no steam escapes,
meaning the mass inside remains perfectly
constant.
Isolated System
An isolated system has a boundary that is perfectly insulated and
completely rigid, preventing the exchange of both mass and energy.
Example: Hot coffee inside a perfectly insulated thermos flask.
❖ No Energy exchange: The vacuum insulation prevents heat
from escaping or entering.
❖ No Mass exchange: The sealed cap prevents any liquid or vapor from
leaving.
Note: A perfectly isolated system is a theoretical ideal; a thermos is an approximation.
Thermodynamical State
The thermodynamical state of a system refers to the exact condition of the system at a specific moment in
time.
This condition is completely described by its macroscopic properties.
For example: if you have a gas in a cylinder, you can fully define its "state" by stating its
current Pressure (P), Volume (V), Temperature (T), and Mass (m).
If any of these macroscopic properties change, the system is said to have undergone a change of state (or
a thermodynamic process).
Thermodynamical Variables
Thermodynamical variables (or coordinates) are the measurable macroscopic quantities used to define the
state of a thermodynamic system.
Also known as State Variables or State Parameters.
Examples: Pressure (P), Volume (V), Temperature (T), and Internal Energy (U).
These variables are broadly categorized into two fundamental types based on their dependency on the
mass/size of the system:
❖ Extensive Variables
❖ Intensive Variables
Extensive vs. Intensive Variables
Extensive Variables
Intensive Variables
Variables whose values depend on the mass
or the size of the system.
Variables whose values are independent of
the mass or size of the system.
If you divide a system in half, the extensive
properties will be halved.
If you divide a system in half, intensive
properties remain the same.
Examples:
Examples:
Mass (m)
Entropy(S)
Pressure (P)
Volume (V)
Temperature (T)
Internal Energy (U)
Density (ρ)
Heat Capacity (C)
Specific Heat Capacity (c)
Thermodynamical Equilibrium
A system is said to be in thermodynamical equilibrium if its macroscopic properties (like pressure,
temperature, volume) do not change with time.
For a system to be in absolute thermodynamic equilibrium, it must simultaneously satisfy three different
types of equilibrium:
Thermal Equilibrium
Temperature is uniform
throughout the system and
surroundings. No net heat
flows.
Mechanical Equilibrium
No unbalanced forces exist
within the system or between
the system and surroundings.
Pressure is uniform.
Chemical Equilibrium
No chemical reactions are
occurring, and the chemical
composition remains constant
throughout.
Variables and Processes
State Variables vs. Path Variables
State Variables (Point Functions)
State variables: are quantities that depend only on the current state of the system,
regardless of the path or process taken to reach that state.
❖ They describe the "now" of the system.
❖ Their change depends strictly on the initial and final states.
Examples: Pressure (P), Volume (V), Temperature (T), Internal Energy (U).
Path Variables (Path Functions)
Path variables are quantities whose values depend on the specific path or sequence of
steps taken during a thermodynamic process.
❖ They describe the transition between states, not the state itself.
❖ You cannot say a system "contains" a certain amount of work or heat; you can only measure the
amount transferred during a process.
Examples:
❖Work Done (∆W):
Depends on how the system expands or compresses.
❖ Heat Exchange (∆Q): Depends on the heating process applied.
State vs. Path:
Imagine climbing a mountain from Base Camp (Initial State) to the Peak
(Final State).
Altitude (State Variable): Your change in altitude is exactly the same
whether you take the steep, direct trail or the long, winding trail. It only
depends on the start and end points.
Distance Traveled (Path Variable): The actual distance your legs walked is vastly different
depending on which path you chose.
Internal Energy (U)
The internal energy (U) of a system is the total energy possessed by
the system due to the microscopic motion and configuration of its
particles (atoms/molecules).
It is the sum of:
Kinetic Energy: Due to translational, rotational, and vibrational motion of molecules.
Potential Energy: Due to intermolecular forces of attraction.
Note: Internal energy is a state variable. We usually measure the change in internal energy (ΔU),
not its absolute value.
Internal Energy: Real vs. Ideal Gas
Ideal Gas
Real Gas
In an ideal gas, there are assumed to be zero
intermolecular forces of attraction.
In a real gas, intermolecular forces do exist.
Therefore,
intermolecular Energy(U) = 0.
Therefore, it possesses both Kinetic Energy and
Potential Energy.
The internal energy of an ideal gas is purely
Kinetic and depends ONLY on its absolute
Temperature (T).
i.e. U = f (T)
The internal energy of a real gas depends on both
Temperature (T) and Volume (V).
i.e. U = f(T, V)
➢ USolid < ULiquid < Ugas.
Thermal Energy vs. Heat (Q)
Thermal Energy is the total kinetic energy of the molecules inside a system.
It is a component of Internal Energy.
Heat (Q) is the energy transferred across the boundary of a system due solely to a
temperature difference between the system and its surroundings.
Heat is energy in transit. It is a path variable.
Once heat enters a system, it ceases to be heat and becomes part of the system's internal
energy.
Example: Holding a hot cup of tea. Energy flows from the hot cup to your cooler hand.
This transferred energy is heat.
Work Done (W) in Thermodynamics
In thermodynamics, Work (W) is the energy transferred across the system boundary due to a macroscopic
driving force other than a temperature difference (like pressure).
It usually involves the expansion or compression of a gas against a resisting force.
Like heat, Work is energy in transit and is a path variable.
Example: Expanding gas in a cylinder pushing a piston outward, driving an engine.
Sign Conventions
Sign Convention:
(Heat Exchange(Q) & Change in Internal Energy ΔU)
Heat Exchange (Q)
Change in Internal Energy (ΔU)
❖ Positive (+Q): Heat is absorbed by the
system from surroundings.
❖ Positive (+ΔU): Internal energy increases
(temperature of ideal gas rises).
❖ Negative (-Q): Heat is rejected (given out)
by the system to surroundings.
❖ Negative (-ΔU): Internal energy decreases
(temperature of ideal gas falls).
Sign Convention:
Work Done (W)
Work Done (W)
❖ Positive (+W): Work done by the system.
❖ This occurs during Expansion (Volume increases). The system expends energy to push the
surroundings (like a piston) outward.
❖ Negative (-W): Work done ON the system.
❖ This occurs during Compression (Volume decreases). The surroundings exert a force to
compress the system.
Work Done During Expansion:
∴.
Consider a fixed amount of gas system is enclosed inside a cylinder fitted with a movable,
frictionless and weightless piston of cross sectional area A. Let P and V be pressure and volume
of the gas inside the cylinder
Work Done Derivation
∴Force exerted by gas on the piston (F) = P × A
When the gas expands, the piston displaces through infinitesimal small displacement dx. The small
work done by gas dW is:
dW = F × dx = PA dx = P dV
∴ dW = P dV
..............
[ As A dx = dV = increased in volume)
(1)
This is the small amount of work done by gas with changing volume dV.
Total Work Done
To find the total work done W as the volume expands from an initial volume V₁ to a final volume V₂, we
integrate the expression:
𝐕𝟐
𝐕𝟐
W = ‫𝑽𝒅 𝐏 𝐕׬ = 𝒘𝒅 𝐕׬‬
𝟏
𝟏
This is the fundamental equation for work done by a fluid undergoing expansion or compression.
If V2 – V1 = + Ve or expansion of gas, W = + Ve
If V2 – V1 = - Ve or compression of gas, W = - Ve.
From P-V Indicator Diagram Indicator Diagram
A P-V diagram (Indicator Diagram) is a graph showing the variation of pressure (P) against volume (V) of a
system undergoing a thermodynamic process.
❖ Y-axis represents Pressure (P).
❖ X-axis represents Volume (V).
❖ Every point on the curve represents a
specific thermodynamical state of the
system.
Work from P-V Diagram
Key Principle:
The total work done by or on a system during a thermodynamic process is equal to the Area under
the P-V diagram bounded by the volume axis.
From figure, Area of the small strip EFGH = EH × HG = P × dV
∴ The area of the strip EFGH = P dV = Work done during a small volume change dV
..........
Thus total work done(W) from initial state A (P1, V1) to the final state B (P2, V2) is
𝑽𝟐
∴ W = ‫ = 𝑽𝒅𝑷 𝑽׬‬Area of ABCD
𝟏
..............
(2)
(1)
❖ If the arrow on the curve points to the right
(Expansion): Volume increases, Work is Positive.
❖ If the arrow points to the left (Compression): Volume
decreases, Work is Negative.
❖ If cyclic process is clockwise, the net work
done (W) is positive.
❖ If cyclic process is anticlockwise, the net
work done (W) is negative.