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College Physics (Urone)
Found in: Page 548
College Physics (Urone)

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

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Short Answer

Which cyclical process represented by the two closed loops, ABCFA and ABDEA, on the PV diagram in the figure below produces the greatest net work? Is that process also the one with the smallest work input required to return it to point A? Explain your responses.

The greatest net work is produced by the process ABDEA. Yes, it has the least work input for reaching point A.

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Definition of work in thermodynamics

Work done in a thermodynamic process is defined as the area under the P-V diagram in moving from initial volume \({{\rm{V}}_{\rm{1}}}\) to \({{\rm{V}}_{\rm{2}}}\).

\({\rm{W = }}\int\limits_{{{\rm{V}}_{\rm{1}}}}^{{{\rm{V}}_{\rm{2}}}} {{\rm{PdV}}} \)

For a closed cyclic process, the work done will then be the area enclosed by the graph of the closed cyclic process.

Comparing the two closed loops

From the diagram, it can be seen that the area of the closed-loop ABDEA is more than that of ABCFA. Hence, the net work produced in the process ABCDA is more than the other.

Work Input

As the input work is needed for two processes- CF for the cyclic process ABCFA and DE for the cyclic process ABDEA. The work needed in processes FA and EA is zero, as there is no change in volume in these processes.

The area under the curve represents the work needed for the process. If we compare the processes CF and DE the area under the curve is smaller for DE. Thus, the cyclic process ABDEA is the one with the least work input.

Most popular questions for Physics Textbooks

(a) How much heat transfer occur to the environment by an electrical power station that uses 1.25×1014J of heat transfer into the engine with an efficiency of 42.0 %(b) What is the ratio of heat transfer to the environment to work output (c) How much work is done?

unreasonable Results

(a) Suppose you want to design a steam engine that has heat transfer to the environment at 270ºC and has a Carnot efficiency of 0.800. What temperature of hot steam must you use? (b) What is unreasonable about the temperature? (c) Which premise is unreasonable?

Explain why a building made of bricks has smaller entropy than the same bricks in a disorganized pile. Do this by considering the number of ways that each could be formed (the number of microstates in each macrostate).

(a) On a winter day, a certain house loses 5.00×108 J of heat to the outside (about 500,000 Btu). What is the total change in entropy due to this heat transfer alone, assuming an average indoor temperature of 21.0 ºC and an average outdoor temperature of 5.00 ºC ? (b) This large change in entropy implies a large amount of energy has become unavailable to do work. Where do we find more energy when such energy is lost to us?

Assume that the turbines at a coal-powered power plant were upgraded, resulting in an improvement in efficiency of \({\bf{3}}.{\bf{32}}\% \). Assume that prior to the upgrade the power station had an efficiency of \({\bf{36}}\% \) and that the heat transfer into the engine in one day is still the same at \({\rm{2}}{\rm{.50 \times 1}}{{\rm{0}}^{{\rm{14}}}}{\rm{J}}\). (a) How much more electrical energy is produced due to the upgrade? (b) How much less heat transfer occurs to the environment due to the upgrade?
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