Thermodynamics Notes
Study Notes
Topics
11Thermal Equilibrium, Temperature & Zeroth Law
Overview
Thermal equilibrium is the condition in which two bodies in contact stop exchanging net heat because they have the same temperature. Temperature is the physical quantity that tells the direction of heat flow: heat flows naturally from higher temperature to lower temperature. The Zeroth Law states that if two systems are separately in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This law makes temperature measurement possible because a thermometer can act as the third system. For NEET, remember that thermal equilibrium does not mean equal heat content or equal internal energy; it means equal temperature and no net heat flow.
- 1Temperature is a state variable, while heat is energy in transit.
- 2A thermometer works by reaching thermal equilibrium with the body whose temperature is measured.
- 3Two objects can have the same temperature but different masses, materials and internal energies.
- 4The Zeroth Law is called zeroth because it is more fundamental than the first and second laws.
- 5Thermal equilibrium is a macroscopic condition; microscopic molecular motion still continues.
Zeroth Law Shortcut
Think: Same as C, same as each other. Thermometer C certifies equality of temperature.
Temperature vs Heat
Temperature tells direction; heat is the energy in motion.
Thermometer Example
A clinical thermometer reads body temperature only after it reaches thermal equilibrium with the body.
Metal Spoon in Tea
A spoon in hot tea becomes warm because heat flows from tea to spoon until thermal equilibrium is reached.
Confusing Equal Temperature with Equal Heat
A bucket and a cup of water at 30°C have the same temperature, but the bucket contains more internal energy.
Using Celsius in Thermodynamic Formulae
Gas-law and Carnot calculations require kelvin, not Celsius.
Used to convert Celsius temperature into absolute temperature scale used in thermodynamics.
Variables
T=absolute temperature in kelvin
t=temperature in degree Celsius
Thermodynamic Systems, State Variables & Equation of State
Overview
A thermodynamic system is the part of the universe chosen for study, while everything outside it is the surroundings. Systems may be open, closed or isolated depending on exchange of mass and energy. The macroscopic condition of a system is described by state variables such as pressure, volume, temperature and internal energy. A state function depends only on the state, not on the path followed. For an ideal gas, pressure, volume and temperature are connected by the equation of state PV = nRT. NEET questions often test whether a quantity is a state variable or a path variable, and whether the system is open, closed or isolated.
- 1A thermodynamic state is fixed when enough independent state variables are known.
- 2For a fixed amount of ideal gas, any two of P, V and T determine the third.
- 3Equilibrium states are represented as points on a P-V diagram.
- 4Quasi-static processes pass through a series of equilibrium states.
- 5Internal energy of an ideal gas depends only on temperature.
Open-Closed-Isolated
Open opens everything; closed closes mass only; isolated isolates both mass and energy.
State vs Path
State is address; path is route. U has an address, Q and W depend on the route.
Pressure Cooker
A pressure cooker is nearly a closed system during cooking because mass exchange is small until steam escapes.
Human Body
The human body is an open thermodynamic system because it exchanges food, gases, heat and work with surroundings.
Calling Heat a State Variable
A system does not contain heat; heat is energy transferred because of temperature difference.
Ignoring Kelvin
Always use absolute temperature in PV = nRT.
Equation of state for an ideal gas connecting pressure, volume, amount and temperature.
Variables
P=pressure of gas
V=volume of gas
n=number of moles
R=universal gas constant
T=absolute temperature
Useful when the number of molecules is given instead of moles.
Variables
N=number of molecules
kB=Boltzmann constant
T=absolute temperature
Heat, Work & Internal Energy
Overview
Heat, work and internal energy are central quantities in thermodynamics. Internal energy is the total microscopic energy of molecules due to random motion and interactions. Heat is energy transferred between system and surroundings because of temperature difference. Work is energy transferred when a macroscopic force acts through displacement, such as gas pushing a piston. In thermodynamics, work done by a gas during expansion is positive in the NCERT convention commonly used for physics: W = ∫P dV. Heat and work are path dependent, but change in internal energy is path independent. For an ideal gas, internal energy depends only on temperature.
- 1Internal energy includes kinetic and potential energies of microscopic particles.
- 2For an ideal gas, intermolecular potential energy is neglected.
- 3Area under a P-V curve gives work done by the gas.
- 4Work is zero in an isochoric process because volume does not change.
- 5Heat supplied can increase internal energy, produce work, or both.
U is Inside
Internal energy is inside the gas; heat and work are ways energy crosses the boundary.
Expansion Positive
When volume expands, gas pushes the world: work by gas is positive.
Bicycle Pump
Air becomes warm during compression because work is done on the gas, increasing its internal energy.
Steam Engine
Steam expands and pushes a piston, converting heat into mechanical work.
Saying Heat is Stored
A body stores internal energy, not heat. Heat exists only during transfer.
Missing Area Meaning
On P-V graphs, the area under the curve, not the slope, gives work.
The area under the curve in a P-V diagram gives work done by gas.
Variables
W=work done by gas
P=pressure of gas
dV=small change in volume
Work done by gas when pressure remains constant.
Variables
P=constant pressure
V1=initial volume
V2=final volume
First Law of Thermodynamics
Overview
The First Law of Thermodynamics is the law of conservation of energy applied to thermal systems. In the NCERT physics sign convention, heat supplied to a system is used partly to increase internal energy and partly to do external work: Q = ΔU + W. If heat is supplied but no work is done, internal energy increases. If a gas expands without heat input, its internal energy decreases. The law does not tell whether a process is naturally possible; that is the role of the second law. NEET problems usually involve identifying signs of Q, W and ΔU for different processes and applying the equation carefully.
- 1The first law connects heat, work and internal energy quantitatively.
- 2It applies to all thermodynamic processes.
- 3Internal energy change is independent of path, while Q and W depend on path.
- 4For ideal gas, ΔU depends only on temperature change.
- 5In a cycle, the net heat supplied equals net work done.
First Law Sentence
Heat given = energy kept + work spent.
Cycle Shortcut
In a complete cycle, U comes home, so ΔU = 0.
Heating Gas in a Cylinder
If gas absorbs 500 J heat and does 200 J work, its internal energy increases by 300 J.
Rapid Expansion
If gas expands adiabatically and does work, its temperature falls because internal energy decreases.
Wrong Sign of Work
Check whether the question uses work done by gas or work done on gas. NCERT physics commonly uses Q = ΔU + W, where W is work by gas.
Applying ΔU = nCvΔT to Any Substance
This simple relation is mainly used for ideal gases in this chapter.
Heat supplied to a system equals increase in internal energy plus work done by the system.
Variables
Q=heat supplied to system
ΔU=change in internal energy
W=work done by system
Since internal energy is a state function, it returns to the initial value after a complete cycle.
Variables
ΔUcycle=net change in internal energy over one cycle
Qnet=net heat absorbed
Wnet=net work done
Thermodynamic Processes: Isothermal, Adiabatic, Isobaric, Isochoric & Cyclic
Overview
A thermodynamic process is a change of a system from one equilibrium state to another. The most important NEET processes are isothermal, adiabatic, isobaric, isochoric and cyclic. In an isothermal process, temperature remains constant and for an ideal gas ΔU = 0. In an adiabatic process, no heat is exchanged and temperature usually changes. In an isobaric process, pressure is constant; in an isochoric process, volume is constant and work is zero. A cyclic process returns to its initial state, so net change in internal energy is zero. P-V graphs are essential because the area under the curve gives work.
- 1Quasi-static processes are slow enough for the system to remain nearly in equilibrium.
- 2Isothermal expansion needs heat input to keep temperature constant.
- 3Adiabatic expansion cools the gas; adiabatic compression heats it.
- 4No work is done in constant volume heating or cooling.
- 5Clockwise P-V cycle gives positive net work by gas.
ISO Words
Iso means same: isothermal same temperature, isobaric same pressure, isochoric same volume.
Adiabatic A
Adiabatic has A for Absent heat: Q = 0.
Vertical Volume
On P-V graph, vertical line means volume is fixed, so isochoric work is zero.
Slow Expansion in Thermal Contact
A gas expanding slowly in contact with a heat reservoir is nearly isothermal.
Sound Wave Compression
Compression and rarefaction in sound waves are approximately adiabatic because they occur rapidly.
Mixing Isothermal and Adiabatic
Isothermal has constant temperature and heat exchange; adiabatic has no heat exchange and temperature generally changes.
Forgetting Work in Isobaric Process
At constant pressure, volume can change, so work is usually not zero.
Wrong Cycle Direction
Clockwise cycle gives positive work by gas; anticlockwise gives negative work by gas.
For a fixed amount of ideal gas at constant temperature.
Variables
P=pressure
V=volume
Work done by an ideal gas during reversible isothermal expansion or compression.
Variables
n=number of moles
R=universal gas constant
T=absolute temperature
V1, V2=initial and final volumes
Heat Capacity, Specific Heat & Mayer Relation
Overview
Heat capacity measures how much heat is required to raise the temperature of a body. Specific heat capacity is heat required per unit mass per unit temperature rise, while molar heat capacity is heat required per mole per unit temperature rise. For gases, heat required depends strongly on the process. At constant volume, supplied heat only increases internal energy, so Cv is used. At constant pressure, heat also does work of expansion, so Cp is greater than Cv. For an ideal gas, Mayer’s relation is Cp - Cv = R. The ratio γ = Cp/Cv is crucial in adiabatic processes and heat engine questions.
- 1Cp is greater than Cv for gases because expansion work is done at constant pressure.
- 2Specific heat depends on material and sometimes temperature.
- 3Molar heat capacity is preferred for gases in thermodynamics.
- 4For monoatomic ideal gas, Cv = 3R/2 and Cp = 5R/2.
- 5For diatomic ideal gas at ordinary temperature, Cv = 5R/2 and Cp = 7R/2.
Cp Greater
P for Push: at constant Pressure the gas Pushes piston, so Cp is larger.
Mayer Memory
Cp is one R more than Cv for an ideal gas: Cp = Cv + R.
Water as Coolant
Water is used in cooling systems because its high specific heat allows it to absorb much heat with small temperature rise.
Gas Heating in Balloon
A heated balloon expands, so some heat increases internal energy and some does work against the atmosphere.
Using Same Heat Capacity for All Processes
For gases, heat capacity depends on the process; use Cv for constant volume and Cp for constant pressure.
Confusing Heat Capacity and Specific Heat
Heat capacity is for the entire body; specific heat is per kg.
Heat required to raise the temperature of a body by one kelvin.
Variables
S=heat capacity
Q=heat supplied
ΔT=temperature change
Heat required depends on mass, specific heat and temperature rise.
Variables
m=mass
c=specific heat capacity
ΔT=temperature change
Second Law, Entropy & Irreversibility
Overview
The First Law permits many energy-conserving processes, but the Second Law decides which processes occur naturally. Heat naturally flows from hot to cold, not cold to hot without external work. No heat engine can convert all absorbed heat into work in a cyclic process. Entropy is a measure of energy dispersal or disorder, and the entropy of an isolated system never decreases. Reversible processes are ideal and can be exactly retraced; real processes are irreversible due to friction, turbulence, finite temperature differences and dissipation. For NEET, focus on Kelvin-Planck and Clausius statements, entropy change, and why 100% efficient heat engines are impossible.
- 1Kelvin-Planck statement: complete conversion of heat from a single reservoir into work is impossible in a cycle.
- 2Clausius statement: heat cannot flow from cold to hot without external work.
- 3Entropy is a state function.
- 4For a reversible process, dS = δQrev/T.
- 5Irreversibility is associated with entropy production.
Second Law Direction
Second law is the traffic rule of heat: hot to cold is allowed naturally; cold to hot needs work.
Entropy
Entropy likes spreading. Energy and matter tend to disperse spontaneously.
Perfume Spreading
Perfume molecules spread through a room spontaneously; they do not collect back into the bottle by themselves.
Ice Melting in Warm Water
Heat flows from warm water to ice, not the reverse, unless work is supplied through a device.
Thinking First Law Forbids All Impossible Processes
The first law only checks energy conservation; the second law checks natural possibility.
Saying Entropy Always Increases for a System
Entropy of a system can decrease, but total entropy of system plus surroundings for an isolated universe cannot decrease.
Entropy change when heat is transferred reversibly at constant temperature.
Variables
ΔS=change in entropy
Qrev=reversible heat transfer
T=absolute temperature
General definition of entropy change for a reversible infinitesimal process.
Variables
dS=small entropy change
δQrev=small reversible heat transfer
T=absolute temperature
Heat Engines, Refrigerators & Heat Pumps
Overview
A heat engine is a cyclic device that absorbs heat from a hot reservoir, converts part of it into work, and rejects the remaining heat to a cold reservoir. Its efficiency is the fraction of absorbed heat converted into work. A refrigerator works in the reverse direction: it removes heat from a cold body and rejects it to a hotter surroundings by using external work. A heat pump is similar but its useful output is heat delivered to the hot region. NEET questions commonly ask for efficiency, coefficient of performance, energy balance, and why an engine cannot have 100% efficiency due to the second law.
- 1A heat engine must operate between at least two reservoirs.
- 2Work output is less than heat absorbed from the source.
- 3A refrigerator does not destroy heat; it transfers heat from cold to hot using work.
- 4Coefficient of performance can be greater than 1.
- 5Efficiency of heat engines is always less than 1.
Engine vs Fridge
Engine gives work; fridge takes work.
COP Can Cross One
COP is not efficiency. It compares moved heat with work input, so it can be greater than 1.
Car Engine
Fuel combustion provides heat; part becomes mechanical work and the rest is rejected through exhaust and radiator.
Home Refrigerator
A refrigerator removes heat from inside the cabinet and releases more heat into the room because electrical work is also added.
Assuming COP is Percentage
COP is a ratio and may exceed 1; do not convert it like efficiency unless asked.
Forgetting Rejected Heat
A heat engine cannot convert all QH into work; some heat QC must be rejected.
Net work delivered by a heat engine in one cycle.
Variables
W=work output
QH=heat absorbed from hot reservoir
QC=heat rejected to cold reservoir
Fraction of heat absorbed that is converted into useful work.
Variables
η=efficiency
W=work output
QH=heat absorbed
QC=heat rejected
Carnot Engine & Carnot Cycle
Overview
The Carnot engine is an ideal reversible heat engine operating between two reservoirs at temperatures TH and TC. Its cycle has four reversible steps: isothermal expansion at TH, adiabatic expansion, isothermal compression at TC and adiabatic compression. It has the maximum possible efficiency for any engine working between the same two temperatures. Carnot efficiency depends only on reservoir temperatures and is given by η = 1 - TC/TH, where temperatures must be in kelvin. No real engine can exceed Carnot efficiency because real engines have irreversibilities such as friction and finite temperature heat transfer. NEET often asks cycle sequence, efficiency and comparison of engines.
- 1During isothermal expansion, engine absorbs heat QH from hot reservoir.
- 2During adiabatic expansion, temperature falls from TH to TC.
- 3During isothermal compression, engine rejects heat QC to cold reservoir.
- 4During adiabatic compression, temperature rises from TC back to TH.
- 5Carnot theorem forms a foundation for thermodynamic temperature scale.
Carnot Sequence
I A I A: Isothermal expansion, Adiabatic expansion, Isothermal compression, Adiabatic compression.
Efficiency Temperature Rule
Hot high, cold low makes efficiency grow: η = 1 - cold/hot.
Efficiency Calculation
An engine between 600 K and 300 K has maximum efficiency 1 - 300/600 = 0.5 or 50%.
Improving Engine Efficiency
Raising the source temperature or lowering the sink temperature increases the theoretical maximum efficiency.
Using Celsius in Carnot Formula
Carnot efficiency must use kelvin temperatures. Using Celsius gives physically wrong results.
Thinking Carnot Engine is Real
Carnot engine is an ideal reversible model; real engines are always less efficient.
Maximum efficiency of a reversible engine operating between hot and cold reservoirs.
Variables
ηCarnot=Carnot engine efficiency
TC=temperature of cold reservoir in kelvin
TH=temperature of hot reservoir in kelvin
For a reversible Carnot engine, heat exchanged is proportional to absolute reservoir temperature.
Variables
QC=heat rejected to cold reservoir
QH=heat absorbed from hot reservoir
TC=cold reservoir temperature
TH=hot reservoir temperature
Calorimetry, Latent Heat & Thermal Exchange
Overview
Calorimetry deals with measurement of heat exchanged between bodies. When hot and cold bodies are mixed in an insulated container, heat lost by the hot body equals heat gained by the cold body, assuming no loss to surroundings. Temperature change without phase change is calculated using Q = mcΔT. During a phase change, temperature remains constant while heat changes the internal molecular arrangement; this heat is called latent heat and is calculated using Q = mL. Although calorimetry is often introduced in thermal properties, it supports thermodynamics by clarifying heat transfer, thermal equilibrium and energy conservation. NEET questions often combine calorimetry with phase change.
- 1A calorimeter is treated as insulated to avoid heat exchange with surroundings.
- 2Specific heat determines how easily temperature changes.
- 3Latent heat of fusion is for solid-liquid transition.
- 4Latent heat of vaporisation is for liquid-gas transition.
- 5Steam at 100°C contains more heat than water at 100°C due to latent heat.
Latent Means Hidden
Latent heat is hidden heat: it changes state without showing temperature rise.
Calorimetry Balance
In an insulated mixture: hot loses exactly what cold gains.
Steam Burns
Steam at 100°C causes more severe burns than water at 100°C because steam releases latent heat on condensation.
Ice in Water
Ice cools a drink effectively because it absorbs heat both to melt and then to warm the melted water.
Adding Temperature Change During Phase Change
During melting or boiling at fixed pressure, temperature remains constant until the phase change is complete.
Ignoring Calorimeter Heat Capacity
If the calorimeter’s water equivalent or heat capacity is given, include its heat gain or loss.
Heat required for temperature change without phase change.
Variables
Q=heat exchanged
m=mass
c=specific heat capacity
ΔT=change in temperature
Heat required for phase change at constant temperature.
Variables
m=mass undergoing phase change
L=specific latent heat
NEET Problem Strategy: Signs, Graphs & Concept Traps
Overview
Thermodynamics NEET problems become easy when you first identify the process, sign convention and known state variables. Always draw or inspect the P-V graph: area under the curve gives work, and enclosed area gives net work in a cycle. Next use the first law Q = ΔU + W and the ideal-gas fact that ΔU depends only on temperature. For engines and refrigerators, apply energy balance before efficiency or COP. For Carnot questions, convert all temperatures to kelvin. Conceptual traps usually involve confusing heat with internal energy, using Celsius, assuming all processes are reversible, or forgetting that second law limits efficiency.
- 1If temperature is unchanged for an ideal gas, internal energy change is zero.
- 2If volume is unchanged, work is zero.
- 3If heat exchange is zero, process is adiabatic.
- 4If a graph is cyclic, net work is the enclosed area.
- 5Efficiency cannot exceed Carnot efficiency for same reservoirs.
- 6COP and efficiency are different quantities.
T-V-Q Cycle
T constant means ΔU zero; V constant means W zero; Q zero means adiabatic.
Graph Rule
Under curve is work; inside cycle is net work.
One-Line First Law Example
If Q = 100 J and gas does W = 40 J, then ΔU = 60 J.
Cycle Example
If a cyclic engine absorbs 800 J and rejects 500 J, work output is 300 J and efficiency is 37.5%.
Not Reading Sign Convention
Some sources use work done on gas. NEET physics NCERT style generally uses work done by gas in Q = ΔU + W.
Skipping Units
Use SI units: pressure in pascal, volume in cubic metre, temperature in kelvin and energy in joule.
Assuming ΔU Depends on Path
Internal energy is a state function; for ideal gas it depends only on temperature.
Use this after identifying W and ΔU from process conditions.
Variables
Q=heat supplied
ΔU=internal energy change
W=work done by gas
Graphical method for work done by gas.
Variables
W=work done by gas
P-V curve=pressure-volume path of the process
Formula Sheet
10Used to convert Celsius temperature into absolute temperature scale used in thermodynamics.
Variables
T=absolute temperature in kelvin
t=temperature in degree Celsius
Relates Fahrenheit and Celsius scales.
Variables
C=temperature on Celsius scale
F=temperature on Fahrenheit scale
Equation of state for an ideal gas connecting pressure, volume, amount and temperature.
Variables
P=pressure of gas
V=volume of gas
n=number of moles
R=universal gas constant
T=absolute temperature
Useful when the number of molecules is given instead of moles.
Variables
N=number of molecules
kB=Boltzmann constant
T=absolute temperature
Connects molar and molecular gas constants.
Variables
NA=Avogadro number
kB=Boltzmann constant
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NEET PYQs — Thermodynamics
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At a certain temperature T(K), during a process, 500 J is absorbed by the system and work of 200 J is done by the system. Then change in internal energy of the system is:
Consider the following reaction: 2A(g) + B(g) → 2D(g) ΔU° = −10 kJ mol⁻¹ and ΔS° = −44 J K⁻¹ at 298 K Identify the correct option with ΔG° for the reaction and spontaneity of the reaction at 298 K. (Given: R = 8.31 J mol⁻¹ K⁻¹)
An electric heater supplies heat to a system at a rate of 100 W. If the system performs work at a rate of 75 J/s, then the rate at which internal energy increases will be:
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