Carnot Cycle: Screencasts

Introduction to the Carnot heat engine (Only watch the first 3 minutes).

We suggest you list the important points in this screencast as a way to increase retention.

Presents calculations for Carnot heat engine.

We suggest you list the important points in this screencast as a way to increase retention.

Important Equations:

Thermal efficiency ($$\eta$$) for the heat engine:

$\eta \equiv -\frac{|\dot{W}|}{\dot{Q}_H} \equiv \frac{work\, output}{heat\, input}$

where $$\dot{W}$$ is the net work generated per time by the engine and $$\dot{Q}_H$$ is the heat added to the engine per time from the high-temperature reservoir. The work is negative for a heat engine.

Carnot heat efficiency in terms of high and low reservoir temperatures:

$\eta _0 \equiv -\frac{|\dot{W}|}{\dot{Q}_H} = 1 + \frac{\dot{Q}_C}{\dot{Q}_H} = 1 – \frac{T_C}{T_H} = \frac{T_H – T_C}{T_H}$

where $$T_C$$ is the temperature of the cold reservoir and $$T_H$$ is the temperature of the hot reservoir.

Coefficient of performance for heat pump/refrigerator:

$COP \equiv \frac{\dot{Q}_C}{\dot{W}}$

where $$\dot{Q}_C$$ is the heat transferred to the heat pump per time from the low-temperature reservoir and $$\dot{W}$$ is the work added per time to the engine.

Coefficient of performance for Carnot heat pump in terms of the high and low reservoir temperatures:

$COP \equiv \frac{\dot{Q}_C}{\dot{W}} = \left( \frac{T_H}{T_C} – 1 \right) ^{-1} = \frac{T_C}{T_H – T_C}$