PREPWISER.
Practise online

Thermodynamics formula sheet

Every formula in the Thermodynamics chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 32 and download the PDF.

Sign in to read all 32Download PDF

Read the first part free. Sign in free with Google to read the rest and download the PDF: 3 A4 pages.3 A4 pages, ready to print.

How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Basics and the first law

Zeroth law
1× asked, last 2026
A↔C,  B↔C ⇒ A↔BA\leftrightarrow C,\ \ B\leftrightarrow C\ \Rightarrow\ A\leftrightarrow B
↔\leftrightarrow = thermal equilibrium; defines temperature.
Intensive and extensive
2× asked, last 2026
extensive÷mass or volume=intensive\text{extensive}\div\text{mass or volume}=\text{intensive}
Extensive: mm, VV, UU, SS. Intensive: PP, TT, ρ\rho, specific heat.
Ideal gas equation
PV=nRT,P1V1T1=P2V2T2PV=nRT,\qquad \frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}
Fixed amount; TT in K. Connected vessels: ∑PV/T\sum PV/T conserved.
Mixing gases in an insulated box
Tf=∑niCV,iTi∑niCV,iT_f=\frac{\sum n_iC_{V,i}T_i}{\sum n_iC_{V,i}}
UU conserved.
First law
13× asked, last 2026
ΔQ=ΔU+W\Delta Q=\Delta U+W
Q>0Q>0 into the gas, W>0W>0 by the gas. UU is a state function; QQ, WW depend on path.
Phase change at constant PP
Q=mL,W=P ΔV,ΔU=mL−P ΔVQ=mL,\qquad W=P\,\Delta V,\qquad \Delta U=mL-P\,\Delta V
ΔV\Delta V from V=m/ρV=m/\rho.
Internal energy of an ideal gas
9× asked, last 2026
ΔU=nCVΔT=nR ΔTγ−1=P2V2−P1V1γ−1\Delta U=nC_V\Delta T=\frac{nR\,\Delta T}{\gamma-1}=\frac{P_2V_2-P_1V_1}{\gamma-1}
Any process (depends on TT only). Cycle: ΔU=0\Delta U=0.
Specific heats
9× asked, last 2026
CV=f2R,CP=CV+R,γ=1+2fC_V=\frac f2R,\qquad C_P=C_V+R,\qquad \gamma=1+\frac2f
γ\gamma: 5/35/3 mono, 7/57/5 diatomic or linear, 4/34/3 non-linear, 9/79/7 vibrating diatomic.
Other equations of state
CP−CV=P(∂V∂T)PC_P-C_V=P\left(\frac{\partial V}{\partial T}\right)_P
When UU depends on TT only (e.g. PV2=RTPV^2=RT).

Practise Thermodynamics questions as you read. Free, and you can start without signing up.

Practise Thermodynamics

23 more formulas in 4 topics

Work and P–V diagrams; Thermodynamic processes; Heat engines, refrigerators and Carnot; and Second law, reversibility and entropy. Read the first part free. Sign in free with Google to read the rest and download the PDF.

Sign in to read the restYou come straight back to this spot.Download the PDF

Work and P–V diagrams

  • Work done by a gas8×
  • Cyclic process12×
  • Lines on V–T and P–T graphs6×
  • Temperature along a path3×

Thermodynamic processes

  • Isochoric7×
  • Isobaric14×
  • Isothermal11×
  • Adiabatic7×
  • Adiabatic relations19×
  • Adiabatic work14×
  • Slopes on a P–V graph4×
  • Comparing work (expansion)2×
  • Polytropic process5×
  • Molar heat capacity of a process6×
  • Expansion coefficient of a gas1×
  • Free expansion2×

Heat engines, refrigerators and Carnot

  • Heat engine5×
  • Carnot engine20×
  • Carnot cycle5×
  • Engines in series4×
  • Refrigerator and heat pump3×

Second law, reversibility and entropy

  • Second law1×
  • Entropy4×

Practise Thermodynamics next

About 150 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

Practise Thermodynamics

Also free on PrepWiser

Spotted a mistake? Write to support@prepwiser.in and we will fix it in the next version.

Version 1, October 2026. Free to share for study, as it is. Please don't sell it or remove the PrepWiser name.

PractiseSign in to read all 32Download PDF
Free with Google, takes a few seconds3 pages, free