I was reading a list of science experiment ideas, and came across one that intrigued me: calculating the efficiency of a sterling engine.(adsbygoogle = window.adsbygoogle || []).push({});

We can say that the efficiency n_th is:

n_th = W_out / Q_in

Assuming we are heating the engine with a beaker of hot water,

Q_in = m * c * [tex]\Delta[/tex]T

But how would we calculate work out? If the engine is making a wheel spin, as most sterling engines do, then we could calculate the work out as a rotational analog of the definition of work:

W_out = [tex]\tau[/tex][tex]\Delta\theta[/tex]

Where [tex]\tau[/tex] is the torque on the wheel, which we could substitute with

[tex]\tau[/tex] = [tex]\alpha[/tex]I

Where [tex]\alpha[/tex] is the angular acceleration, and I is the moment of inertia of the wheel.

Thus, we must be able to calculate the angular acceleration of the wheel, as well as its moment of inertia. Is this the easiest way to do this? How else could we measure the effieciency of a sterling engine?

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# Calculating Work Out for a Sterling Engine

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