Question 1

How do you calculate Carnot cycle efficiency?

Accepted Answer

Carnot efficiency is calculated as η = 1 − T_C / T_H, where T_H is the absolute temperature of the hot reservoir (in Kelvin) and T_C is the absolute temperature of the cold reservoir (in Kelvin). For example, with T_H = 600 K and T_C = 300 K, η = 1 − 300/600 = 50%. This represents the maximum theoretical efficiency of any heat engine operating between those two temperatures.

Question 2

What are the four processes of the Carnot cycle?

Accepted Answer

The Carnot cycle consists of: (1) Isothermal expansion at T_H — the working fluid absorbs heat Q_H while expanding at constant temperature; (2) Adiabatic expansion — the fluid expands without heat transfer, temperature drops from T_H to T_C; (3) Isothermal compression at T_C — the fluid rejects heat Q_C while being compressed at constant temperature; (4) Adiabatic compression — the fluid is compressed without heat transfer, temperature rises from T_C back to T_H.

Question 3

What is the COP of a Carnot heat pump?

Accepted Answer

The coefficient of performance of a Carnot heat pump is COP_hp = T_H / (T_H − T_C). For example, with T_H = 330 K (57°C) and T_C = 280 K (7°C), COP_hp = 330 / 50 = 6.6, meaning the heat pump delivers 6.6 times the energy it consumes as electricity. Real heat pumps achieve lower COP due to irreversibilities.

Question 4

Why is the Carnot cycle a rectangle on a T-S diagram?

Accepted Answer

In a T-S diagram, isothermal processes (constant T) appear as horizontal lines because entropy changes at constant temperature, while reversible adiabatic (isentropic) processes appear as vertical lines because entropy is constant. Since the Carnot cycle consists of two isothermal and two isentropic processes, the resulting shape is a rectangle. The area of this rectangle equals (T_H − T_C) × ΔS, which equals the net work W output.

Carnot Cycle Efficiency Calculator

Theory