Thermodynamics (Class 11): the laws, cycles and engines
Thermodynamics tells how heat turns into work and why no engine is perfect. Compress a gas, run a Carnot cycle on the p–V diagram and see how heat flows through a rod, all in one browser tab.
NCERT Class 11 Physics, Chapters 10 and 11 (Thermal Properties of Matter, Thermodynamics). Every lab below runs in 3D in your browser or on a phone, in English and Hindi.
Try the labs
Isothermal, adiabatic, isobaric, isochoric processes and the Carnot cycle · plan · Chapter 11
To study the first law of thermodynamics for an ideal gas undergoing isothermal, adiabatic, isobaric and isochoric processes, and the working of a Carnot engine.
Carnot engine and p-V diagram · plan · Chapter 11
To study a Carnot engine: heat absorbed, heat rejected, work per cycle, efficiency and power, and compare with a real engine.
Clement-Desormes: ratio of specific heats gamma · plan · Chapter 11
To determine the ratio of specific heats γ = C_p/C_v of a gas by the Clement–Desormes method.
Calorimetry: specific heat by method of mixtures · plan · Chapter 10
To determine the specific heat capacity of a metal by the method of mixtures.
Black-body radiation: Wien and Stefan laws · plan · Chapter 10
To study black-body radiation: the Planck spectrum, Wien displacement law (λ_max T = b) and the Stefan–Boltzmann law (P = σAT⁴).
Heat conduction through a rod · plan · Chapter 10
To study conduction of heat along a rod, the steady-state temperature gradient and thermal conductivity.
Heating curve of ice to steam: latent heat · plan · Chapter 10
To draw the heating curve of water through its three phases and determine the specific heat capacities and latent heats of fusion and vaporisation from it.
Linear expansion of a metal rod · plan · Chapter 10
To study linear thermal expansion and determine the coefficient of linear expansion α of a rod.
Newton's law of cooling · plan · Chapter 10
To study how a hot body cools in surroundings and verify Newton's law of cooling.
Thermal stress in a clamped rod · plan · Chapter 10
To understand thermal expansion of solids and the thermal stress developed when the expansion is prevented.
Free expansion and entropy · plan · Chapter 11
To understand irreversibility and entropy through the free expansion of a gas into vacuum, and why the reverse process is practically impossible.
Joule's paddle wheel: mechanical equivalent of heat · plan · Chapter 11
To determine the mechanical equivalent of heat J by converting mechanical work into heat (Joule's experiment).
Otto and Diesel engine cycles on a P-V diagram · plan · Chapter 11
To study the Otto and Diesel cycles on the P–V diagram and see how efficiency depends on the compression ratio and γ.
Refrigerator and heat pump (COP) · plan · Chapter 11
To study refrigerators and heat pumps as reversed heat engines and understand the coefficient of performance (COP).
Heat, work and the first law
The heat given to a system equals the increase in its internal energy plus the work it does, ΔQ = ΔU + W. For an ideal gas the internal energy depends only on the temperature.
On a p–V diagram the work done equals the area under the curve.
ΔQ = ΔU + WW = ∫ p dVΔU = n Cv ΔTCp − Cv = R
Processes
In an isothermal process pV is constant. In an adiabatic process no heat enters or leaves, so pV^γ is constant and the gas cools as it expands. Isochoric and isobaric processes keep V and p constant.
pV = constant (isothermal)pV^γ = constant (adiabatic)W = nRT ln(V₂/V₁) (isothermal)W = (p₁V₁ − p₂V₂)/(γ − 1) (adiabatic)
Engines and the second law
A heat engine takes Q₁ from a hot source, does work W and rejects Q₂ to a cold sink. No engine working between two temperatures is more efficient than the Carnot engine. A refrigerator is an engine run backwards.
In the chapter on thermal properties the labs add specific heat, latent heat, conduction and Newton's law of cooling.
η = W/Q₁ = 1 − Q₂/Q₁η (Carnot) = 1 − T₂/T₁COP = Q₂ / W
Frequently asked questions
Why is an adiabatic curve steeper than an isothermal one?
In the adiabatic case the temperature falls as the gas expands, so the pressure drops faster than in the isothermal case.
Can the efficiency of an engine be 100%?
No. The second law says some heat must go to the cold sink, and even a Carnot engine has η = 1 − T₂/T₁ < 1.
What is a reversible process?
One that can be reversed by an infinitesimal change in the conditions, with the system always near equilibrium. Real processes are irreversible.
Why does a gas cool in free expansion?
An ideal gas does not. Its temperature stays the same, but its entropy increases.