MotionLab

Carnot Efficiency Calculator

The absolute ceiling on how efficiently any heat engine can convert thermal energy to work.

Hot reservoir temp (K)

Cold reservoir temp (K)

Efficiency (%)

η = 1 − Tc/Th

COP (refrigerator): 1

What you entered

Hot reservoir temp (K): 600Cold reservoir temp (K): 300

1
η = 1 − Tc ÷ Th
1 − 300 ÷ 600= 0.5
2
Efficiency percentage
0.5 × 100= 50%
3
COP (refrigerator) = Tc ÷ (Th − Tc)
300 ÷ (600 − 300)= 1

Result

Efficiency (%): 50

A Carnot engine between 600 K and 300 K has a maximum efficiency of 50%. As a refrigerator, COP = 1.

Maximum possible heat engine efficiency

Carnot efficiency is 1 minus the cold temperature divided by the hot, both in kelvin. No real engine can beat it.

Hot reservoir (K)	Cold reservoir (K)	Efficiency	As a percentage	Refrigerator COP
373	273	0.2681	26.81	2.730
500	300	0.4000	40.00	1.500
600	400	0.3333	33.33	2.000
800	300	0.6250	62.50	0.600
1000	300	0.7000	70.00	0.429

Temperatures must be absolute - using Celsius gives nonsense, and it is the commonest error in the topic. The first row is a steam engine between boiling and freezing water, capped at 26.81% however well it is built, which is why early steam engines were so inefficient and why raising the hot side matters more than anything else. Real engines fall well short of Carnot because of friction, heat loss and irreversibility: a modern car engine reaches perhaps 30% against a Carnot limit near 60%. The COP column runs the cycle backwards as a refrigerator, and note it falls as the temperature gap widens.

No real engine beats Carnot

The Carnot efficiency sets a hard upper limit dictated by thermodynamics — no heat engine, no matter how cleverly designed, can exceed η = 1 − Tc/Th. Real engines (car engines, power plants) typically achieve 30–60% of this theoretical maximum due to friction, irreversible processes, and heat losses.

Why bigger temperature differences matter

The formula shows that efficiency improves when the hot reservoir gets hotter or the cold reservoir gets colder — this is why power plants use superheated steam (high Th) and why rocket engines in the vacuum of space (low effective Tc) can be very efficient.

Frequently asked questions

A coal power plant operates between 550°C (823 K) and 30°C (303 K). What's the maximum possible efficiency?

η_Carnot = 1 − Tc/Th = 1 − 303/823 = 0.632 = 63.2%. Real coal plants achieve about 33-40% — roughly half of Carnot. The gap is due to friction, incomplete combustion, and irreversible heat transfer.

Why can't any engine be 100% efficient?

Carnot's theorem shows η = 1 − Tc/Th. For 100% efficiency, Tc would need to be 0 K (absolute zero), which is physically impossible to reach. Even a 'perfect' engine must reject some heat to the cold reservoir — this is a fundamental law of thermodynamics, not an engineering limitation.

How does a heat pump's COP relate to Carnot efficiency?

A heat pump's maximum COP = Th/(Th − Tc) = 1/η_Carnot. Between 5°C outside and 20°C inside: COP_max = 293/15 = 19.5. Real heat pumps achieve COP 3-5. A COP of 4 means 4 kWh of heat delivered per 1 kWh of electricity — far better than resistive heating.