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Condition for minimum work done by a compressor?

Updated: 8/18/2019
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12y ago

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Isentropic work, i.e completely reversible work

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Q: Condition for minimum work done by a compressor?
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If the work was done correctly, no.


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They have the same units- Joules - so can be equated. Work is something actually done, and in doing work energy is expended, but you can also talk of doing work to store energy. For example in running a compressor to fill a cylinder with compressed gas, energy is supplied to the compressor motor, work is done by the compressor, and the result is stored energy in the gas. Fuels such as coal have potential or stored energy, which can be released to do work. So I think the fundamental is energy, but when energy is used, work results. Hope that makes sense!


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Angle between force and displacement to get minimum work?

The work done by a force is the dot product of the force and the displacement of the point of application of the force i.e.component of force in the direction of displacement * displacementorcomponent of displacement in the direction of force * forcelet W be the work done. Then :W = F.SW = |F|*|S|*cos(θ) ---- equation 1where F and S are force and displacement in vector form and |F|, |S| are their magnitudes respectively. cos(θ) is the angle between line of action of force vector and displacement vector.It is clear from the equation 1 that work will be minimum when cos(θ) is minimum. It is known from trigonometry that minimum value of cos(θ) is -1 which is for angle 1800 or π radians. So work done will be minimum when angle between force and displacement vector is π radians or 1800 i.e. when point of application of force is displaced exactly opposite to the direction of application of force.I appreciate the last attempt to answer the question, but I think it is wrong. The answer should be 90°, because although cos180° = -1, the negative sign in- FScos180° only signifies that the work done has taken away energy from the system, or it signifies that the work is done in the opposite direction, implying that work is done. When the angle is 90°, on the other hand, work done = 0, ie, no work is done at all. Thus the answer should be 90°.(The above answers define minimum work differently.The first answers is if minimum work is negative work, therefore if you do work in the opposite direction of the displacement, the work you do is negative and is less than 0. Minimum work here is the work that is the lowest number.The second answer defines minimum work as the magnitudeof the work done being minimized. Since magnitude is always positive, minimum work in this case would always be zero. Which one is correct depends on the situation you are dealing with.)


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