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INDIANA UNIVERSITY, DEPARTMENT OF PHYSICS, P309 LABORATORY

Laboratory #26: Efficiency of Steam Engine and Electric Generator

Goal: Experimental study of the conversions of heat to mechanical power and of mechanical power to electrical power. Methods to measure mechanical power. Efficiency of conversion. Equipment: Jensen steam engine, variac, AC power meter, Prony brake, stroboscope, variac, power meter, electric generator, variable resistor box. (A) Physics:

Machines that convert heat to mechanical power operate between two temperature reservoirs at temperatures T1 and T2. The efficiency of such a machine is the ratio of heat energy input to mechanical energy output. From the Second Law of Thermodynamics follows that the best possible efficiency ?max is [FEY64]

max = T1 - T2 T1

.

(1)

For a steam engine, T1 ~ 390K (steam under pressure), and T2 ~ 350K (steam at exhaust). With this, the best efficiency is ?max=10%. The efficiency of a real steam engine is often much lower than ?max. The mechanical power delivered by the rotating shaft of an engine is

P =

,

(2)

where t is the torque on the shaft, and ? is the angular velocity, or ? =2p f, with f the frequency of rotation. Mechanical engineers use a device called a "Prony brake" to apply a torque to the shaft of an engine that can be varied and measured. The device uses friction; it is shown schematically in Fig.1. Question: derive eq.2

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(B)

Experiment:

Operate the steam engine. It is important to fill the tank with water to two thirds on the view glass. Since the water is heated electrically, it is easy to measure the input power. Set the variac for the steam heater to 110V and measure the output power for different loads (tensions in the Prony brake). Measure the output power for a number of input power settings. Calculate the efficiencies. Connect the electrical generator, run the steam engine at the 110V setting, and measure the output power of the generator. Vary the load resistor and decide if there is a load for which the power output is a maximum. Calculate the efficiency of the generator. (C) [FEY64] Reference: Feynman Lectures on Physics, Addison-Wesley, Reading, MA, 1964, vol.I, chapter 44, p.44-7.

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