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SLec11m

# SLec11m - Lecture 11 Carnot Heat Engines Consider a heat...

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Lecture 11: Carnot Heat Engines Consider a heat machine that operates in cycles , each consisting of several steps called strokes The Carnot engine is formed by four (reversible) strokes: 1. The gas is expanded isothermally from ( P 1 , V 1 , T 1 ) to ( P 2 , V 2 , T 1 ) 2. The gas is expanded adiabatically from ( P 2 , V 2 , T 1 ) to ( P 3 , V 3 , T 2 ) 3. The gas is compressed isothermally from ( P 3 , V 3 , T 2 ) to ( P 4 , V 4 , T 2 ) 4. The gas is compressed adiabatically from ( P 4 , V 4 , T 2 ) to ( P 1 , V 1 , T 1 ) The four strokes are termed Carnot cycle (shown right) The system is assumed to be perfect, so that maximum work is done: This work is equal the negative of the area.

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For the isothermal expansions (Stroke 1 and 3) of an ideal gas : Stroke 1: (V 2 >V 1 ), q 1 >0 (heat is taken from the surroundings), Stroke 3: (V 3 <V 4 ), q 3 <0 (heat is returned to the surroundings). For the adiabatic processes with δ q=0 (Stroke 2 and 4), we have
The total work done in one Carnot cycle is then We can define the efficiency of the engine by We can see the constant efficiency lines in the T 1 -T 2 -plot Complete conversion of heat to work is impossible.

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We can invert the direction of motion in the Carnot cycle, i.e. we to add work –w T
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SLec11m - Lecture 11 Carnot Heat Engines Consider a heat...

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