<< Chapter < Page Chapter >> Page >

Conceptual questions

A great deal of effort, time, and money has been spent in the quest for the so-called perpetual-motion machine, which is defined as a hypothetical machine that operates or produces useful work indefinitely and/or a hypothetical machine that produces more work or energy than it consumes. Explain, in terms of heat engines and the first law of thermodynamics, why or why not such a machine is likely to be constructed.

Got questions? Get instant answers now!

One method of converting heat transfer into doing work is for heat transfer into a gas to take place, which expands, doing work on a piston, as shown in the figure below. (a) Is the heat transfer converted directly to work in an isobaric process, or does it go through another form first? Explain your answer. (b) What about in an isothermal process? (c) What about in an adiabatic process (where heat transfer occurred prior to the adiabatic process)?

Figure a shows a piston attached to a movable cylinder which is attached to the right of another gas filled cylinder. The heat Q sub in is shown to be transferred to the gas in the cylinder as shown by a bold arrow toward it. The force of the gas on the moving cylinder with the piston is shown as F equals P times A shown as a vector arrow pointing toward the right. The change in internal energy is marked in the diagram as delta U sub a equals Q sub in. Figure b shows a piston attached to a movable cylinder which is attached to the right of another gas filled cylinder. The force of the gas has moved the cylinder with the piston by a distance d toward the right. The change in internal energy is marked in the diagram as delta U sub b equals negative W sub out. The piston is shown to have done work by change in position, marked as F d equal to W sub out. Figure c shows a piston attached to a movable cylinder which is attached to the right of another gas filled cylinder. The piston attached to the cylinder is shown to reach back to the initial position shown in figure a. The distance d is traveled back and heat Q sub out is shown to leave the system as represented by an outward arrow. The force driving backward is shown as a vector arrow pointing to the left, labeled F prime. F prime is shown less than F. The work done by the force F prime is shown by the equation W sub in equal to F prime times d.
Got questions? Get instant answers now!

Would the previous question make any sense for an isochoric process? Explain your answer.

Got questions? Get instant answers now!

We ordinarily say that Δ U = 0 size 12{DU=0} {} for an isothermal process. Does this assume no phase change takes place? Explain your answer.

Got questions? Get instant answers now!

The temperature of a rapidly expanding gas decreases. Explain why in terms of the first law of thermodynamics. (Hint: Consider whether the gas does work and whether heat transfer occurs rapidly into the gas through conduction.)

Got questions? Get instant answers now!

Which cyclical process represented by the two closed loops, ABCFA and ABDEA, on the PV size 12{ ital "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 figure shows a graph of pressure versus volume. The pressure is along the Y axis and the volume is plotted along the X axis. The graph consists of a rectangle, A B C F, superimposed on a slightly larger rectangle, A B D E. The lines A B, C F, and D E are parallel to the X axis and lines B C D and A F E are parallel to the Y axis.
The two cyclical processes shown on this PV diagram start with and return the system to the conditions at point A, but they follow different paths and produce different amounts of work.
Got questions? Get instant answers now!

A real process may be nearly adiabatic if it occurs over a very short time. How does the short time span help the process to be adiabatic?

Got questions? Get instant answers now!

It is unlikely that a process can be isothermal unless it is a very slow process. Explain why. Is the same true for isobaric and isochoric processes? Explain your answer.

Got questions? Get instant answers now!

Problem exercises

A car tire contains 0 . 0380 m 3 size 12{0 "." "0380"" m" rSup { size 8{3} } } {} of air at a pressure of 2 . 20 × 10 5 N/m 2 size 12{2 "." "20"´"10" rSup { size 8{5} } " N/m" rSup { size 8{2} } } {} (about 32 psi). How much more internal energy does this gas have than the same volume has at zero gauge pressure (which is equivalent to normal atmospheric pressure)?

6 . 77 × 10 3 J size 12{6 "." "77" times "10" rSup { size 8{3} } `J} {}

Got questions? Get instant answers now!

A helium-filled toy balloon has a gauge pressure of 0.200 atm and a volume of 10.0 L. How much greater is the internal energy of the helium in the balloon than it would be at zero gauge pressure?

Got questions? Get instant answers now!

Steam to drive an old-fashioned steam locomotive is supplied at a constant gauge pressure of 1 . 75 × 10 6 N/m 2 size 12{1 "." "75"´"10" rSup { size 8{6} } " N/m" rSup { size 8{2} } } {} (about 250 psi) to a piston with a 0.200-m radius. (a) By calculating P Δ V size 12{PDV} {} , find the work done by the steam when the piston moves 0.800 m. Note that this is the net work output, since gauge pressure is used. (b) Now find the amount of work by calculating the force exerted times the distance traveled. Is the answer the same as in part (a)?

(a) W = P Δ V = 1 . 76 × 10 5 J size 12{W=PΔV= {underline {1 "." "76" times "10" rSup { size 8{5} } " J"}} } {}

(b) W = Fd = 1 . 76 × 10 5 J size 12{W= ital "Fd"= ital "PAd"= {underline {1 "." "76" times "10" rSup { size 8{5} } " J"}} } {} . Yes, the answer is the same.

Got questions? Get instant answers now!

A hand-driven tire pump has a piston with a 2.50-cm diameter and a maximum stroke of 30.0 cm. (a) How much work do you do in one stroke if the average gauge pressure is 2 . 40 × 10 5 N/m 2 size 12{2 "." "40"´"10" rSup { size 8{5} } " N/m" rSup { size 8{2} } } {} (about 35 psi)? (b) What average force do you exert on the piston, neglecting friction and gravitational force?

Got questions? Get instant answers now!

Calculate the net work output of a heat engine following path ABCDA in the figure below.

A graph is shown of pressure versus volume, with pressure on the Y axis and volume on the X axis. A parallelogram connects four points are on the graph, A, B, C, and D. A is at y equals 2 point 6 times 10 to the six newtons per meter squared and x equals 1 point zero times ten to the minus three meters cubed. A downward sloping line connects A to B. B is at y equals 2 point zero, x equals four. A vertical line connects B to C. C is at y equals zero point 6, x equals 4. A line connects C to D. D is at y equals one point zero, x equals one point zero. A vertical line connects D to A. A diagonal line also connects D and B.

W = 4 . 5 × 10 3 J size 12{W=4 "." 5 times "10" rSup { size 8{3} } `J} {}

Got questions? Get instant answers now!

What is the net work output of a heat engine that follows path ABDA in the figure above, with a straight line from B to D? Why is the work output less than for path ABCDA? Explicitly show how you follow the steps in the Problem-Solving Strategies for Thermodynamics .

Got questions? Get instant answers now!

Unreasonable Results

What is wrong with the claim that a cyclical heat engine does 4.00 kJ of work on an input of 24.0 kJ of heat transfer while 16.0 kJ of heat transfers to the environment?

W size 12{W} {} is not equal to the difference between the heat input and the heat output.

Got questions? Get instant answers now!

(a) A cyclical heat engine, operating between temperatures of 450º C size 12{"450"°C} {} and 150º C size 12{"150"°C} {} produces 4.00 MJ of work on a heat transfer of 5.00 MJ into the engine. How much heat transfer occurs to the environment? (b) What is unreasonable about the engine? (c) Which premise is unreasonable?

Got questions? Get instant answers now!

Construct Your Own Problem

Consider a car's gasoline engine. Construct a problem in which you calculate the maximum efficiency this engine can have. Among the things to consider are the effective hot and cold reservoir temperatures. Compare your calculated efficiency with the actual efficiency of car engines.

Got questions? Get instant answers now!

Construct Your Own Problem

Consider a car trip into the mountains. Construct a problem in which you calculate the overall efficiency of the car for the trip as a ratio of kinetic and potential energy gained to fuel consumed. Compare this efficiency to the thermodynamic efficiency quoted for gasoline engines and discuss why the thermodynamic efficiency is so much greater. Among the factors to be considered are the gain in altitude and speed, the mass of the car, the distance traveled, and typical fuel economy.

Got questions? Get instant answers now!

Questions & Answers

Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
Giovani Reply
What is meant by dielectric charge?
It's Reply
what happens to the size of charge if the dielectric is changed?
Brhanu Reply
omega= omega not +alpha t derivation
Provakar Reply
u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
Abrar
do to be peaceful with any body
Brhanu Reply
the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
Saeed Reply
if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
Saeed
define variable velocity
Ali Reply
displacement in easy way.
Mubashir Reply
binding energy per nucleon
Poonam Reply
why God created humanity
Manuel Reply
Because HE needs someone to dominate the earth (Gen. 1:26)
Olorunfemi
why god made humenity
Ali
Is the object in a conductor or an insulator? Justify your answer. whats the answer to this question? pls need help figure is given above
Jun Reply
ok we can say body is electrically neutral ...conductor this quality is given to most metalls who have free electron in orbital d ...but human doesn't have ...so we re made from insulator or dielectric material ... furthermore, the menirals in our body like k, Fe , cu , zn
Abrar
when we face electric shock these elements work as a conductor that's why we got this shock
Abrar
how do i calculate the pressure on the base of a deposit if the deposit is moving with a linear aceleration
ximena Reply
why electromagnetic induction is not used in room heater ?
Gopi Reply
room?
Abrar
What is position?
Amoah Reply
What is law of gravition
sushil Reply
Practice Key Terms 6

Get the best College physics for ap... course in your pocket!





Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics for ap® courses' conversation and receive update notifications?

Ask