gen-define-the-carnot-cycle-and-give-one-short-worked-example-bccf

Define the Carnot cycle and give one short worked example.

# Carnot Cycle The **Carnot cycle** is an idealized thermodynamic cycle that represents the most efficient heat engine possible operating between two temperature reservoirs. It consists of four reversible processes: 1. **Isothermal expansion** (at high temperature T_H) - absorbs heat Q_H 2. **Adiabatic expansion** - temperature drops from T_H to T_C 3. **Isothermal compression** (at low temperature T_C) - rejects heat Q_C 4. **Adiabatic compression** - temperature rises from T_C back to T_H The **Carnot efficiency** is: η = 1 - T_C/T_H --- ## Worked Example A Carnot engine operates between a hot reservoir at 500 K and a cold reservoir at 300 K. If it absorbs 1000 J from the hot reservoir, find: - The efficiency - The work output - The heat rejected **Solution:** **Efficiency:** η = 1 - T_C/T_H = 1 - 300/500 = 1 - 0.6 = **0.4 or 40%** **Work output:** W = η × Q_H = 0.4 × 1000 J = **400 J** **Heat rejected:** Q_C = Q_H - W = 1000 - 400 = **600 J** (Or alternatively: Q_C/Q_H = T_C/T_H, so Q_C = 1000 × 300/500 = 600 J)