Carnot Cycle

The Carnot cycle is an idealized reversible heat engine cycle operating between two fixed temperature reservoirs: a hot reservoir at temperature Th and a cold reservoir at temperature Tc (absolute, K). It consists of two reversible isothermal processes (heat transfer at constant temperature) and two reversible adiabatic (isentropic) processes. Because it is reversible and operates between fixed thermal reservoirs, the Carnot cycle has the maximum possible thermal efficiency for any engine operating between those two temperatures. Key implications: (1) The cycle is wholly determined by Th and Tc for efficiency and heat ratios. (2) For a reversible cycle the net entropy change of system plus reservoirs is zero; equivalently Qh/Th = Qc/Tc. (3) No irreversible engine operating between the same two reservoirs can exceed Carnot efficiency; if an engine matches Carnot efficiency it must be reversible.

Governing FormulaUse absolute temperatures (K). Main relations for a Carnot engine/refrigerator/heat pump: - Carnot engine efficiency: η = 1 - Tc/Th - Heat ratio (reversible): Qh/Qc = Th/Tc (equivalently Qh/Th = Qc/Tc) - Work per cycle: W = Qh - Qc = η Qh - Carnot refrigerator coefficient of performance (COP_R): COP_R = Qc/W = Tc/(Th - Tc) - Carnot heat pump coefficient of performance (COP_HP): COP_HP = Qh/W = Th/(Th - Tc) - Reversible entropy balance per cycle: ΔS_total = Qh/Th - Qc/Tc = 0 (Assume ideal reversible operation and negligible kinetic/potential energy changes; SI units: J, K.)

Knowledge Check

10 Questions

1.Which sequence of processes correctly describes the ideal Carnot cycle operating as a heat engine?

2.What is the expression for the maximum (Carnot) thermal efficiency of an engine operating between a hot reservoir at Th and a cold reservoir at Tc (both in Kelvin)?

3.For a reversible Carnot engine, which relation between the magnitudes of heat exchanged with the hot reservoir Qh and cold reservoir Qc is correct?

4.A Carnot engine operates between Th = 600 K and Tc = 300 K. What is its maximum possible thermal efficiency?

5.A Carnot engine absorbs Qh = 5000 J from a reservoir at Th = 500 K and rejects heat to Tc = 300 K. What is the work output per cycle W (in J)?

6.Which expression gives the coefficient of performance (COP) of an ideal Carnot refrigerator operating between Th and Tc (Kelvin)?

7.A Carnot refrigerator operates between Th = 293 K (room) and Tc = 263 K. What is its ideal COP (to two decimal places)?

8.What is the net entropy change of the system plus reservoirs after one complete reversible Carnot cycle?

9.Which statement about real engines and the Carnot cycle is correct?

10.A reversible heat pump (Carnot heat pump) delivers heat to a warm interior at Th = 350 K while rejecting to an outside sink at Tc = 280 K. What is its ideal coefficient of performance (COP_HP)?