Thermodynamics: study guide

Key ideas

Thermodynamics tracks heat, work and internal energy. The first law is energy conservation, the second law says heat engines cannot be perfectly efficient, and temperatures must be in kelvin.

• The ideal gas law PV = nRT links pressure, volume, amount and absolute temperature. Always use kelvin (K = °C + 273.15).
• Heat needed to change a temperature is Q = mcΔT. A phase change takes heat at constant temperature: Q = mL.
• The first law is ΔU = Q − W, where W is the work done by the system.
• No engine working between T_h and T_c can exceed the Carnot efficiency 1 − T_c ÷ T_h. Entropy of an isolated system never decreases.

Key equations

• PV = nRT
• Q = mcΔT
• ΔU = Q − W
• η_Carnot = 1 − T_c ÷ T_h
• ΔS = Q ÷ T
• P = kAΔT ÷ d

Worked example

A heat engine runs between 500 K and 300 K. The maximum (Carnot) efficiency is 1 − 300 ÷ 500 = 0.40, or 40 %. If it takes 1000 J from the hot reservoir per cycle, it can do at most 400 J of work and must discard at least 600 J to the cold reservoir.

Common mistakes

• Putting temperatures in °C into the gas law or the Carnot formula. They need kelvin.
• Forgetting the sign of work: work done by the gas is positive in ΔU = Q − W, and work done on the gas is negative.
• Treating heat and temperature as the same quantity. Heat is energy transferred; temperature measures the average energy of the particles.

Practice

Test yourself with practice questions on this topic: Thermodynamics