JEE Thermodynamics Cheat Sheet

Key Definitions

• Thermodynamics: Study of energy transformations and heat transfer.

• System: The part of the universe under study (e.g., gas in a cylinder).

• Surroundings: Everything outside the system.

Important Formulas

• First Law of Thermodynamics:

  ΔU = Q - W
  

• ΔU = Change in internal energy

• Q = Heat added to the system

• W = Work done by the system

• Work Done (Constant Pressure):

  W = PΔV
  

• W = Work done

• P = Pressure

• ΔV = Change in volume

• Efficiency of Heat Engine:

  η = (W_out / Q_in) = 1 - (T_C / T_H)
  

• η = Efficiency

• W_out = Work output

• Q_in = Heat input

• T_C = Temperature of cold reservoir

• T_H = Temperature of hot reservoir

Critical Concepts

• Isothermal Process: Temperature remains constant (ΔU = 0).

• Adiabatic Process: No heat exchange (Q = 0).

• Cyclic Process: System returns to initial state (ΔU = 0).

• Entropy (S): Measure of disorder; ΔS ≥ 0 for irreversible processes.

Common Mistakes to Avoid

• Confusing work done on vs. work done by the system.

• Forgetting to convert temperatures to Kelvin when using gas laws.

• Misapplying the sign convention in the First Law of Thermodynamics.

Quick Memory Tricks/Mnemonics

• "Q = W + ΔU": Remember "Q" as heat, "W" as work, and "ΔU" as energy change. Think of it as "Heat in = Work out + Energy change".

• "Cyclic = No Change": Cyclic processes have no change in internal energy (ΔU = 0).

Key Diagrams

• PV Diagram: Represents pressure vs. volume for different processes.

  P
  |
  |       / (Isothermal)
  |      /
  |     / (Adiabatic)
  |    /
  |   /_________________ V
  

• Carnot Cycle: Idealized cycle showing efficiency.

  T_H -----> (Q_in) -----> T_C
   |                             |
   |                             |
   | <----- (W_out) <-----------
  

Tip: Always sketch PV diagrams for processes to visualize work done and understand thermodynamic cycles.