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Question: A steam engine delivers \(5.4\times 10^8\) J of work per minute and services \(3.6\times 10^9\) J of...

A steam engine delivers 5.4×1085.4\times 10^8 J of work per minute and services 3.6×1093.6\times 10^9 J of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute?

Explanation

Solution

Hint: Efficiency of any machine or a process is the useful work done from the total heat taken in or the energy spent during that process or by the machine. And the energy wasted is the part of energy that failed to get converted into the work done by the engine.

Complete step by step solution:
The energy required by the steam engine per minute to perform the required work is delivered by the boiler.

So, input energy or the heat supplied to the engine per minute by the boiler =3.6×109= 3.6\times 10^9 J

And, output energy or the work done per minute by the engine =5.4×108=5.4\times 10^8 J

Thus, efficiency of the engine, η=output energyinput energy=5.4×1083.6×109=0.15\eta = \dfrac{\text{output energy}}{\text{input energy}}=\dfrac{5.4\times 10^8}{3.6\times 10^9}=0.15

Hence, percentage efficiency of the engine =15%=15\%

And the amount of energy wasted per minute = Input energy – Output energy =3.6×109−5.4×108=3.06×1093.6\times 10^9 - 5.4\times 10^8 = 3.06\times 10^9 J.

Additional information:
A hypothetical machine that can do work for infinitely long time without any energy source or use of energy is called a perpetual motion machine. These are generally classified into three types.

1.)Perpetual motion machines of first kind: These kinds of machines produce work without an energy requirement and hence are imaginary. It violates the law of conservation of energy.
2.)Perpetual motion machine of second kind: The complete energy supplied is converted into useful work without any wastage of energy, and as it does not violate the law of conservation of energy, but violates the second law of thermodynamics.
3.)Perpetual motion machine of third kind: This kind of machine completely eliminates the possibility of friction or any dissipated forces and can maintain to be in motion forever due to its inertia.
As already stated, these kinds of machines are impossible to make and are just hypothetical.

Note: In machines, a major part of energy wasted is in the form of heat generated due to the presence of resistance between different parts of the machine. The efficiency is the ratio of output energy to the input energy and should not be mistaken.