21Thermodynamics

📚
THERMODYNAMICS
▢ Introduction:
❖ Definition: Thermodynamics deals with conversion of heat into mechanical energy

Table 1: Thermodynamic Variables

Feature
Intensive variables
Extensive variables
Dependence
Do not depend on size or amount of substance
Depend on size or amount of substance
Depend on
Nature of substance
Amount of system
Examples
Temperature, pressure, density, refractive index, surface tension, boiling point, melting point
Mass, volume, entropy, enthalpy, free energy
▢ Zeroth Law of Thermodynamics:
❖ Statement: If two bodies are separately in thermal equilibrium with a third body, then they are also in thermal equilibrium with each other
❖ Formula: If \(T_A=T_C\) and \(T_B=T_C\), then \(T_A=T_B\)
❖ Importance: Basis of temperature measurement
▢ Work:
❖ Definition: Work is done by gas during expansion and work is done on gas during compression

Table 1: Thermodynamic Work

Point
Description / Formula
Work during expansion
Work done by system = positive
Work during compression
Work done on system = negative
Depends on
Path, initial state and final state
PV diagram
Work done = area under PV curve
Formula
\(W=\int_{V_1}^{V_2}P\,dV\)
Cyclic clockwise process
Work done positive
Cyclic anticlockwise process
Work done negative
Net work in cycle
Area enclosed by PV diagram
Order of work done
\(W_{isobaric}>W_{isothermal}>W_{adiabatic}>W_{isochoric}\)
▢ Heat:

Table 1: Heat in Thermodynamics

Point
Description
Nature
Path dependent
Heat entering system
Positive
Heat leaving system
Negative
▢ Internal Energy:
❖ Symbol: \(U\)

Table 1: Internal Energy

Point
Description
Nature
State function
Depends on
Initial and final state only
Does not depend on
Path
Main dependence
Temperature
Cyclic process
\(\Delta U=0\)
Order
\(U_{gases}>U_{liquids}>U_{solids}\)
Ideal gas
Internal energy depends only on temperature
Real gas
Internal energy depends on temperature and volume
▢ First Law of Thermodynamics:
❖ Meaning: Law of conservation of energy
❖ Statement: Heat supplied to a system is used to increase internal energy and to do external work
❖ Formula: \(\Delta Q=\Delta U+\Delta W\)

Table 1: Sign Convention

Quantity
Positive
Negative
\(\Delta Q\)
Heat supplied to system
Heat extracted from system
\(\Delta U\)
Increase in internal energy
Decrease in internal energy
\(\Delta W\)
Expansion / work done by system
Compression / work done on system
▢ Thermodynamic Processes:
❖ Reversible vs Irreversible:

Table 1: Reversible and Irreversible Processes

Feature
Reversible process
Irreversible process
Definition
Changes in heat and work are exactly retraced in reverse direction
Path for heat and work is not retraced
Nature
Ideal process
Natural process
Occurrence
Almost impossible in nature
Processes in nature are irreversible
Examples
Ideal slow frictionless process
Pouring milk into tea, stirring, work against friction
❖ Isothermal Process:
◉ Definition: Temperature remains constant
◉ Condition: Change should be very slow
◉ Equation: \(PV=constant\)
◉ First Law: \(\Delta Q=\Delta W\)
◉ Internal Energy: \(\Delta U=0\)
◉ Work Done: \(W=nRT\ln\frac{V_2}{V_1}=nRT\ln\frac{P_1}{P_2}=\Delta Q\)
◉ Important Points:
  • •
    Obeys Boyle's law
  • •
    Work done depends on temperature and expansion ratio
  • •
    In cyclic and isothermal processes, change in internal energy is zero
❖ Adiabatic Process:
◉ Definition: No heat exchange with surroundings
◉ Conditions:
  • •
    Wall of container must be perfectly insulating
  • •
    Change must be sudden
◉ Heat Exchange: \(\Delta Q=0\)
◉ Equations:
  • •
    \(PV^\gamma=constant\)
  • •
    \(TV^{\gamma-1}=constant\)
  • •
    \(T^\gamma P^{1-\gamma}=constant\)
◉ First Law: \(0=\Delta U+\Delta W\Rightarrow \Delta U=-\Delta W\)
◉ Work Done: \(W=\frac{1}{1-\gamma}(P_2V_2-P_1V_1)=\frac{nR}{1-\gamma}(T_2-T_1)=-\Delta U\)
◉ Entropy: \(\Delta S=\frac{\Delta Q}{T}=0\)
◉ Important Points:
  • •
    Work done in adiabatic change depends only on change in temperature
  • •
    During adiabatic expansion, final pressure is less than isothermal expansion
  • •
    During adiabatic compression, final pressure is more than isothermal compression
❖ Isochoric / Isometric Process:
◉ Definition: Volume remains constant
◉ Condition: \(\Delta V=0\)
◉ Law: Obeys Gay-Lussac's law
◉ Work Done: \(W=0\)
◉ First Law: \(\Delta Q=\Delta U\)
◉ Heat: \(\Delta Q=nC_V\Delta T\)
❖ Isobaric Process:
◉ Definition: Pressure remains constant
◉ Condition: \(\Delta P=0\)
◉ Law: Obeys Charles law
◉ First Law: \(\Delta Q=\Delta U+\Delta W\)
◉ Formula: \(nC_P\Delta T=nC_V\Delta T+P\Delta V\)
◉ Work Done: \(W=P\Delta V=nR\Delta T\)
◉ Ratio: \(\Delta Q:\Delta U:\Delta W=(f+2):f:2\)
▢ Slopes and Elasticities:

Table 1: Slope of PV Curves

Process
Equation
Slope
Isothermal
\(PV=constant\)
\(\left(\frac{dP}{dV}\right)_{iso}=-\frac{P}{V}\)
Adiabatic
\(PV^\gamma=constant\)
\(\left(\frac{dP}{dV}\right)_{adi}=-\gamma\frac{P}{V}\)
Relation
—
Adiabatic slope = \(\gamma\times\) isothermal slope

Table 2: Elasticity of Gases

Process
Elasticity
Isothermal elasticity
\(E_{iso}=P\)
Adiabatic elasticity
\(E_{adi}=\gamma P\)
Isochoric elasticity
\(E_{choric}=\infty\)
Isobaric elasticity
\(E_{baric}=0\)
❖ Important Point: Adiabatic curve is steeper than isothermal curve
▢ Internal Energy in Processes:

Table 1: Change in Internal Energy

Process
\(\Delta U\)
Isobaric
Positive during heating
Isothermal
Zero
Adiabatic expansion
Negative
Cyclic
Zero
Order
\(\Delta U_{isobaric}>\Delta U_{isothermal}>\Delta U_{adiabatic}\)
▢ Second Law of Thermodynamics:

Table 1: Statements of Second Law

Statement
Meaning
Kelvin statement
It is impossible for a cyclic heat engine to convert whole heat extracted from a reservoir completely into work
Clausius statement
Heat cannot flow from colder body to hotter body by itself without external agency
❖ Important Points:
  • •
    Whole work can be converted into heat
  • •
    Whole heat cannot be converted into work
  • •
    Heat naturally flows from hot body to cold body
▢ Heat Engine:
❖ Definition: Device that continuously converts heat energy into mechanical work through cyclic process
❖ Working:
  • •
    Working substance takes heat \(Q_1\) from source
  • •
    Converts part of heat into work \(W\)
  • •
    Rejects remaining heat \(Q_2\) to sink
  • •
    Returns to initial state
  • •
    \(\Delta U=0\) for complete cycle

Table 1: Heat Engine Formulae

Quantity
Formula
Heat rejected
\(Q_2=Q_1-W\)
Work done
\(W=Q_1-Q_2\)
Efficiency
\(\eta=\frac{W}{Q_1}\times100\)
Efficiency
\(\eta=\frac{Q_1-Q_2}{Q_1}\times100\)
Efficiency
\(\eta=\left(1-\frac{Q_2}{Q_1}\right)\times100\)
Carnot efficiency
\(\eta=\left(1-\frac{T_2}{T_1}\right)\times100\)
❖ Efficiency Increase:
  • •
    Increase temperature of source
  • •
    Decrease temperature of sink
▢ Carnot Engine:
❖ Definition: Ideal reversible heat engine working on Carnot cycle
❖ Parts:
  • •
    Hot reservoir / source
  • •
    Cylinder with insulating wall
  • •
    Perfectly conducting base
  • •
    Perfect gas as working substance
  • •
    Frictionless insulated piston
  • •
    Non-conducting stand
  • •
    Sink
❖ Carnot Cycle:

Table 1: Four Strokes of Carnot Cycle

Step
Process
Path
1
Isothermal expansion
AB
2
Adiabatic expansion
BC
3
Isothermal compression
CD
4
Adiabatic compression
DA
❖ Efficiency:

Table 1: Carnot Engine Efficiency

Quantity
Formula / Point
Efficiency
\(\eta=\frac{W}{Q_1}\times100\)
Efficiency
\(\eta=\left(1-\frac{Q_2}{Q_1}\right)\times100\)
Temperature form
\(\eta=\left(1-\frac{T_2}{T_1}\right)\times100\)
Heat-temperature relation
\(\frac{Q_1}{Q_2}=\frac{T_1}{T_2}\)
Between steam point and ice point
\(\eta=26.81\%\)
❖ Carnot Theorem: No irreversible engine can have efficiency greater than Carnot reversible engine working between same hot and cold reservoirs
❖ Important Points:
  • •
    Efficiency depends only on source temperature \(T_1\) and sink temperature \(T_2\)
  • •
    Efficiency is independent of nature of working substance
  • •
    Carnot engine is most efficient engine
  • •
    Efficiency cannot be 100% because sink temperature can never be 0 K
  • •
    All reversible heat engines working between same hot and cold reservoirs have same efficiency
  • •
    Change in entropy of working substance in Carnot cycle is zero because it returns to initial state
  • •
    Carnot cycle contains only two isothermal and two adiabatic processes
▢ Types of Heat Engines:
❖ External vs Internal Combustion:

Table 1: Combustion Engines

Feature
External combustion engine
Internal combustion engine
Fuel burning
Fuel burnt outside main cylinder
Fuel burnt inside main cylinder
Examples
Steam engine
Petrol engine, diesel engine
❖ Steam Engine:

Table 1: Steam Engine

Point
Description
Working substance
Steam
Cycle
Rankine cycle
Use
Powerful engine; drags long trains
Nature
Less efficient and heavy
Efficiency
10% to 20%
❖ Petrol Engine:

Table 1: Petrol Engine

Point
Description
Cycle
Otto cycle
Working substance
Air 98% + petrol 2%
Use
Light vehicles, scooters, cars, aeroplanes
Efficiency
40% to 50%
Engine type
Four-stroke engine
◉ Four Strokes:
  1. Charging stroke
  2. Compression stroke → adiabatic compression
  3. Working / power stroke → adiabatic expansion
  4. Exhaust stroke
❖ Diesel Engine:

Table 1: Diesel Engine

Point
Description
Discovered by
Rudolf Diesel
Working substance
Air 98% + diesel 2%
Efficiency
55% to 70%
Nature
Very heavy engine
Engine type
Four-stroke engine
Spark
Does not require spark
◉ Four Strokes:
  1. Charging stroke
  2. Compression stroke → adiabatic compression
  3. Working / power stroke → adiabatic expansion
  4. Exhaust stroke
❖ Petrol and Diesel Engine Efficiency:
◉ Formula: \(\eta=1-\left(\frac{V_2}{V_1}\right)^{\gamma-1}\)
◉ Compression Ratio Form: \(\eta=1-\left(\frac{1}{\rho}\right)^{\gamma-1}\)
◉ Symbols:
  • •
    \(\gamma=\frac{C_p}{C_v}\) of air
  • •
    \(\rho=\frac{V_1}{V_2}\) = compression ratio
◉ Important Points:
  • •
    Petrol and diesel engines have air as working substance
  • •
    Petrol and diesel oil are used for ignition
  • •
    Useful work is done in third stroke
  • •
    Third stroke is called power stroke
▢ Refrigerator / Heat Pump:
❖ Definition: Heat engine working in reverse direction
❖ Working:
  • •
    Working substance takes heat \(Q_2\) from lower temperature body \(T_2\)
  • •
    External work \(W\) is supplied
  • •
    Heat \(Q_1=Q_2+W\) is rejected to hot body/surrounding at \(T_1\)
❖ Refrigerant: Freon, ammonia, etc.

Table 1: Refrigerator Formulae

Quantity
Formula
Heat rejected
\(Q_1=Q_2+W\)
Work input
\(W=Q_1-Q_2\)
Coefficient of performance
\(\beta=\frac{Q_2}{W}\)
COP
\(\beta=\frac{Q_2}{Q_1-Q_2}\)
Temperature form
\(\beta=\frac{1}{\frac{T_1}{T_2}-1}\)
❖ Open Refrigerator Door: If refrigerator door is kept open inside a room, room temperature increases
▢ Read and Digest:

Table 1: Important Thermodynamics Points

Fact
Point
Milk poured into tea and stirred
Irreversible process
Work done against friction
Irreversible process
Isobaric process ratio
\(\Delta Q:\Delta U:\Delta W=(f+2):f:2\)
Cyclic process
\(\Delta U=0\)
Isothermal process
\(\Delta U=0\)
Isothermal work
Depends on temperature and expansion ratio
Adiabatic work
Depends only on change in temperature
Ideal gas internal energy
Depends only on temperature
Real gas internal energy
Depends on temperature and volume
Increase Carnot efficiency
Increase \(T_1\) or decrease \(T_2\)
Reversible engines between same reservoirs
Same efficiency
Carnot engine
Most efficient engine
Four-stroke heat engine
Power obtained only in third stroke
Same compression volume range
Final pressure in adiabatic compression > isothermal compression
Carnot cycle
Two isothermal + two adiabatic processes
▢ High-Yield Recall:

Table 1: Thermodynamics One-Liners

Fact
Answer
Thermodynamics
Heat ↔ mechanical energy
Intensive variables
Temperature, pressure, density
Extensive variables
Mass, volume, entropy, enthalpy
Zeroth law
Basis of thermal equilibrium
Work done by gas
Positive during expansion
Work done on gas
Negative during compression
Work in PV diagram
\(W=\int P\,dV\)
Clockwise cyclic process
Positive work
Anticlockwise cyclic process
Negative work
Heat entering system
Positive
Heat leaving system
Negative
Internal energy
State function
First law
\(\Delta Q=\Delta U+\Delta W\)
Isothermal process
\(T=constant,\ \Delta U=0\)
Isothermal equation
\(PV=constant\)
Isothermal work
\(W=nRT\ln\frac{V_2}{V_1}\)
Adiabatic process
\(\Delta Q=0\)
Adiabatic equation
\(PV^\gamma=constant\)
Adiabatic work
\(W=\frac{P_2V_2-P_1V_1}{1-\gamma}\)
Isochoric process
\(V=constant,\ W=0\)
Isochoric first law
\(\Delta Q=\Delta U\)
Isobaric process
\(P=constant\)
Isobaric work
\(W=P\Delta V\)
Adiabatic slope
\(\gamma\times\) isothermal slope
Isothermal elasticity
\(P\)
Adiabatic elasticity
\(\gamma P\)
Kelvin statement
Whole heat cannot be converted into work
Clausius statement
Heat cannot flow cold → hot by itself
Heat engine work
\(W=Q_1-Q_2\)
Heat engine efficiency
\(\eta=\left(1-\frac{Q_2}{Q_1}\right)\times100\)
Carnot efficiency
\(\eta=\left(1-\frac{T_2}{T_1}\right)\times100\)
Carnot cycle
2 isothermal + 2 adiabatic
Carnot engine between ice and steam point
26.81%
Steam engine cycle
Rankine cycle
Petrol engine cycle
Otto cycle
Diesel engine
No spark required
Power stroke
Third stroke
Petrol/diesel efficiency
\(\eta=1-\left(\frac{1}{\rho}\right)^{\gamma-1}\)
Refrigerator
Reverse heat engine
Refrigerator COP
\(\beta=\frac{Q_2}{Q_1-Q_2}\)
Refrigerator COP temperature form
\(\beta=\frac{1}{T_1/T_2-1}\)
Q1.
In P-V graph, which curve represents adiabatic process?
Image 1
📅CEE MBBS 2025
Q2.
Heat equation ΔU = ΔQ + ΔW represents
📅CEE MBBS 2025
Q3.
First law of thermodynamics is based on
📅CEE MBBS 2025
Q4.
Which process help to generate power stroke in petrol engine?
📅CEE Nursing 2024
Q5.
The change of entropy (ΔS) in an adiabatic process is:
📅CEE Nursing 2024
Q6.
Which of the following best describes the second law of thermodynamics?
📅CEE Nursing 2024
Q7.
Decreasing order of work done during an expansion process:
📅CEE MBBS 2024B
Q8.
Which of the following sets of temperature of source and sink has maximum efficiency?
📅CEE MBBS 2024B
Q9.
Which of the following is the equation for an adiabatic process?
📅CEE MBBS 2024a
Q10.
An isothermal process is a thermodynamic process in which which quantity remains constant?
📅CEE MBBS 2022
Q11.
Which process helps generate the power stroke in an engine?
📅CEE MBBS 2022
Q12.
A refrigerator works between 0°C and 27°C. Its coefficient of performance is:
📅CEE MBBS 2021
Q13.
Which is incorrect?
📅CEE MBBS 2021
Q14.
The efficiency of Carnot engine is 50% and temperature of sink is 500 K. If the temperature of source is kept constant and its efficiency raised to 60% then the required temperature of the sink will be:
📅CEE BDS 2024
Q15.
Which one is correct for adiabatic process?
📅CEE BDS 2023
Q16.
The first law of thermodynamics is a statement of:
📅CEE BDS 2023
Q17.
If one mole of an ideal gas at STP is heated through 1 K, the work done by the gas in heat unit will be:
📅CEE BDS 2021
Q18.
If a gas is allowed to expand adiabatically against external pressure:
📅CEE BDS 2021
Q19.
A refrigerator has to transfer an average of 263 J of heat per second from −10°C to 25°C. The average power consumed by the refrigerator is:
📅CEE BDS 2021
Q20.
An inventor claims that an engine consumes \(1\,\mathrm{g/s}\) of fuel of calorific value \(2\,\mathrm{kcal/g}\) and delivers \(10\,\mathrm{kW}\) of useful power. Which statement is correct?
📅BP 2010
Q21.
Two containers A and B with frictionless pistons hold the same ideal gas at the same initial temperature \(T\) and volume \(V\), but with masses \(m_A\) and \(m_B\). Each expands isothermally to \(2V\). If the pressure drops are \(\Delta P\) and \(1.5\Delta P\), respectively, what is the relation between the masses?
📅BP 2009
Q22.
Which thermodynamic process occurs at constant temperature while pressure and volume may change?
📅IOM 2012
Q23.
An ideal Carnot refrigerator removes heat at a rate of \(263\,\mathrm{J/s}\) from a chamber at \(-10^\circ\mathrm C\) and rejects it into a room at \(25^\circ\mathrm C\). Find its minimum required input power.
📅IOM 2010/2009
Q24.
An ideal gas expands adiabatically and performs positive work against an external pressure. What happens to its internal energy?
📅MOE 2009
Q25.
Find the efficiency of a Carnot heat engine operating between \(127^\circ\mathrm C\) and \(27^\circ\mathrm C\).
📅MOE 2011
Q26.
A Carnot heat engine has a source at \(327^\circ\mathrm C\) and a sink at \(27^\circ\mathrm C\). Find its efficiency.
📅MOE 2012
Q27.
One mole of an ideal gas has \(\gamma=C_p/C_v=1.4\). During adiabatic compression, its temperature rises from \(27^\circ\mathrm C\) to \(35^\circ\mathrm C\). Find the increase in internal energy (take \(R=8.31\,\mathrm{J/(mol\,K)}\)).
📅MOE 2012
Q28.
A Carnot engine has efficiency \(1/5\). When the sink temperature is lowered by \(45\,\mathrm K\), its efficiency becomes \(1/3\), with source temperature unchanged. Find its initial sink temperature.
📅MOE 2014
Q29.
A Carnot engine has efficiency \(20\%\). Lowering its sink temperature by \(45\,\mathrm K\) raises its efficiency to \(33\frac13\%\). Find the initial sink temperature.
📅MOE 2014
Q30.
For an ideal gas undergoing isothermal expansion, which energy relation is correct?
📅KU 2014
Q31.
A system receives \(1500\,\mathrm{cal}\) of heat and does \(1000\,\mathrm J\) of work on its surroundings. Find its change in internal energy, taking \(1\,\mathrm{cal}=4.2\,\mathrm J\).
📅IOM 2014
Q32.
Which condition defines an adiabatic thermodynamic process?
📅KU 2013
Q33.
A Carnot heat engine operates between reservoirs at \(800\,\mathrm K\) and \(400\,\mathrm K\). If its work output per cycle is \(800\,\mathrm J\), how much heat does it absorb from the hot reservoir?
📅KU 2013
Q34.
What remains constant during an isothermal process?
📅KU 2009
Q35.
During adiabatic compression of an ideal gas, external forces do \(250\,\mathrm J\) of work *on the gas*. What is its change in internal energy?
📅IE 2012
Q36.
For a fixed amount of ideal gas with temperature-dependent internal energy, which relation gives its internal-energy change when \(C_V\) is constant, including during an adiabatic process?
📅IE 2012
Q37.
A Carnot engine has efficiency \(10\%\) between two reservoirs. If it is operated reversibly as a refrigerator between those same reservoirs and consumes \(10\,\mathrm J\) of work, how much heat does it extract from the cold reservoir?
📅TE 2013
Q38.
An ideal gas expands adiabatically and performs positive work on the surroundings. What happens to its internal energy?
📅MOE 2009
Q39.
A Carnot engine absorbs \(3000\,\mathrm{kcal}\) from a source at \(627^\circ\mathrm C\) and rejects heat into a sink at \(27^\circ\mathrm C\). Find the engine’s work output (take \(1\,\mathrm{kcal}=4200\,\mathrm J\)).
📅MOE 2010
Q40.
For an ideal gas undergoing an isothermal process with nonzero heat exchange, what is the formal heat capacity \(C=\delta Q/dT\) of the process?
📅IOM 1997
Q41.
Which statement about thermodynamics is incorrect?
📅IOM 1997
Q42.
A heat engine undergoes a *clockwise rectangular cycle* on a \(P\)-\(V\) diagram, bounded by pressures \(P\) and \(3P\), and volumes \(V\) and \(4V\). What is the net work done in one cycle?
📅Graph-based question
Q43.
One mole of an ideal gas at STP is heated through \(1\,\mathrm K\) *at constant pressure*. Find its work done in calories, taking \(R=8.31\,\mathrm{J/(mol\,K)}\) and \(1\,\mathrm{cal}=4.184\,\mathrm J\).
📅MOE Curriculum
Q44.
A Carnot engine absorbs \(300\,\mathrm{cal}\) from a hot reservoir at \(500\,\mathrm K\) and rejects \(150\,\mathrm{cal}\) to the sink. Find the sink temperature.
📅MOE 2065
Q45.
What is the maximum efficiency of a heat engine operating between \(300^\circ\mathrm C\) and \(30^\circ\mathrm C\)?
📅MOE 2061
Q46.
An ideal gas undergoes a reversible adiabatic process. What relation connects its absolute temperature \(T\) and pressure \(P\), where \(\gamma=C_p/C_v\)?
📅MOE 2000
Q47.
If an ideal gas expands adiabatically while doing positive work, its internal energy:
📅KU 2008
Q48.
For a fixed quantity of ideal gas, internal energy depends only on:
📅KU 2008
Q49.
A Carnot engine working between \(800\,\mathrm K\) and \(500\,\mathrm K\) has the same efficiency as another operating between \(x\,\mathrm K\) and \(600\,\mathrm K\). Find \(x\).
📅IE 2004
Q50.
Engine A works reversibly between \(700\,\mathrm K\) and \(650\,\mathrm K\); engine B works reversibly between \(350\,\mathrm K\) and \(300\,\mathrm K\). Which is more efficient?
📅Bangladesh 2009