Theory of Thermodynamic Variables of Rubber Band Heat Engine

Transcription

1 Journal of Physis: onferene Series PAPER OPEN AESS Theory of Thermodynami Variales of Ruer Band Heat Engine To ite this artile: Nurhidayah Muharayu et al 016 J. Phys.: onf. Ser Related ontent - Struture and Evolution of Single Stars: Physis of gas and radiation J MaDonald - omment Dan N Vollik - Undergraduate thermodynamis and lak holes J Dunning-Davies View the artile online for updates and enhanements. This ontent was downloaded from IP address on 11/1/017 at 09:41

2 Journal of Physis: onferene Series 739 (016) doi: / /739/1/01091 Theory of Thermodynami Variales of Ruer Band Heat Engine Nurhidayah Muharayu 1,a, idayani1,, Khairurrijal1, 1 Master Program in Physis Teahing, Faulty of Mathematis and Natural Sienes, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 4013, Indonesia Department of Physis, Faulty of Mathematis and Natural Sienes, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 4013, Indonesia a muharayu@gmail.om, widayani@fi.it.a.id, krijal@fi.it.a.id Astrat. Ruer and heat engine is a heat engine that is easily applied in the experiment. However, to get the data from the experimental results are required a formulation that is ale to aommodate the data, so that it will e otained an aurate value. e show and analyze the variales thermodynami formulation of ruer and heat engine to aommodate the experimental data, so that the equation of state, heat, work and effiieny are not only studied theoretially ut also experimentally. The engine s effiieny is alulated for an idealized ut reasonale model. The engine s work yle is ompared with a arnot yle, and it is shown to e equivalent to the arnot yle as an extremely ideal limiting ase. e measured the fore law parameters for a working model, and we otained the effiieny of this model. Index Term: Thermodynamis, Ruer Band Heat Engine 1. Introdution Ruer and have interesting thermodynami harateristis that an e used to develop heat engine and refrigeration yles [1]. If most of the solid material will extend when heated, then the ruer and shows different properties, whih will ontrat when heated. By utilizing the thermal properties of the ruer and, then a lot of researh is made to study ruer ands as material onversion of heat engine to hange heat to mehanial energy [-5]. As an ideal gas, ruer and also has a thermodynami variales, suh as equation of state, heat apaity, arnot yle, work, and effiieny. In the learning proess, thermodynami variales of ruer and have een researhed [6-8]. However, they did not onsider aout tehnial matters that may our in experiments to determine the formula of work and heat engine effiieny, so in this paper, we will e explained thermodynami variales of ruer and y onsidering the tehnial aspets to otain the value of work and optimum effiieny when the experiment is done.. Ruer Band Heat Engine The asi design of ruer and heat engine using speifi thermodynami harateristis of a ruer and. To oserve the proess of onverting heat into mehanial energy, then the heat engine is designed to rotate as in Figure 1. ontent from this work may e used under the terms of the reative ommons Attriution 3.0 liene. Any further distriution of this work must maintain attriution to the author(s) and the title of the work, journal itation and DOI. Pulished under liene y td 1

3 Journal of Physis: onferene Series 739 (016) doi: / /739/1/01091 Figure 1. Design of Ruer Band Heat Engine [9] As seen in Figure 1, the engine will rotate when the ul lamp turned on. The heat from the ul auses the hange in tension of the alloons and hanges the position of the enter of mass of heat engine system. This proess has resulted in an imalane of heat engine system. As for the rotating diretion of the engine shown in Figure. Figure. Illustrations of heat engine; R is the radius of the wheel and R 0 is the position of the enter mass due to hanges in tension of ruer and heat engine. 3. The Thermodynamis of Ruer Band As an ideal gas, ruer and also has thermodynami variales, suh as the equation of state, heat apaity, arnot yle, work, and effiieny [1, 8, 10-13]. For ruer and, equation of state an e written as, 0 KT (1) 0 with is tension (N) and 0 is initial length (m), is final length (under tension), K is a onstant that depends on the temperature of the elasti material (N / K), and T is the temperature (K). First law of thermodynamis is used to get another thermodynami variales, suh as heat apaity, heat energy, and work of ruer and as Equation.

4 Journal of Physis: onferene Series 739 (016) doi: / /739/1/01091 and du = đq + đ () đ = τ d (3) where is energy hange in the system du, đq is heat energy, đ is the work, and d is the hange in length of ruer and when the temperature hanged. Equation () is the first law of thermodynamis is used to desrie the ruer and heat engine system and Equation (3) desries the work done y the system. Equation () and (3) will produe two onstants, i.e heat apaity at a onstant length ( ) and heat apaity at a onstant tension (τ). U (4) T (5) where α is length extensivity. 4. Heat of Ruer Band Heat Engine Heat energy is the energy that out and into the system. Heat energy from the heat reservoir with high temperature is alled the heat in and the heat energy out of the system towards the old reservoir with low temperature is alled the heat out. To alulate the heat of eah proess, a,, d and d a, as shown in Figure for a ruer and heat engine, will e alulated heat values of the four proesses that will e a heat engine yle in the ruer and system. The proesses that our in this yle is a quasistati proess like the arnot yle, i.e two adiaatis and two isothermal. Beause U = U (T, ), then Equation () and (3) an e rewritten as in equation (6). For the adiaati proess, eause d 0 then Equation (6) eomes, đq = ( U ) dt + ( U ) d d (6) T T Q dt (7) a T T Q dt (8) d For isothermal proess, eause dt = 0 and tension (τ) is hanged, so that Equation (6) eomes, Q d (9) Beause = (T, τ), then d an e defined as d dt d (10) T T Sustituting Equation (1) and (10) to Equation (3), it is otained, Q (, T) dt d (11) T T Equation (11) is a general equation that shows the heat reeived y the system in the elasti material, while isothermal proess is a proess where the value of dt = 0, so that equation (11) eomes, 3

5 Journal of Physis: onferene Series 739 (016) doi: / /739/1/01091 Q d (1) T Sustituting Equation (10) to Equation (1) then we make integral of it, will e otained a heat value of isothermal proess. Q f i (13) AY Y is the Young's modulus and the magnitude is 3KT0 Y (14) A A Taking the assumption that the value of Y = Y 0 = onstant, where Y 0 is the Young's modulus at τ = 0, then 3KT Y (15) A From the aove, the heat ours in the proess and da is, Q (16) H Qda a d (17) 5. ork of Ruer Band Heat Engine Assuming that no hange of energy in one yle in the system, then the work of ruer and heat engine an e written a dt (18) d T T dt (19) da (0) H a d (1) 6. Effiieny of Ruer Band Heat Engine The effiieny of heat engine is defined as, () ith a d da and Qin Qa Q, we otained Q in a a d da (3) Q Q 4

6 Journal of Physis: onferene Series 739 (016) doi: / /739/1/ KT H T T H dt H a d (4) 7. omparison with Past Ruer Band Heat Engine Both equations of work and effiieny of a ruer and heat engine otained is the equations whose data is more easily oserved through experimentation. So the value of work and effiieny of the alulation results will e more aurate. Unlike the ase with employment equality and effiieny are alulated y Mullen [4] for whih data are diffiult to oserve experimentally, so the equations are more theoretial ones. 8. onlusion e have otained the equations of thermodynami variales of ruer and heat engine. The equations make the data from the experiment y using ruer and heat engine is more easily to e alulated. Referenes [1] Gerlah, D.., J. Alvarado., E. M Mina., T. A Newell (00) : Analysis Of Elastomer Refrigeration yles, [] Roundy, D dan Mihael R (013) : Exploring the thermodynamis of a ruer and, Amerian Journal of Physis, 81, 0. [3] Savarino, G dan M. R. Fish (1991) : A general physis laoratory investigation of the thermodynamis of a ruer and, Amerian Journal of Physis, 59, [4] Mullen, J.G., George.., dan John K (1975) : Thermodynamis of a simple ruer and heat engine, Amerian Journal of Physis, 43, 349. [5] Brown, J.B. (1963) : Thermodynamis of a ruer and, Amerian Journal of Physis, 31, 397. [6] Muharayu, N., idayani., Risa S., and Khairurrijal (014) : Designing of earning y Analogy on an Elasti Heat Engine as an Enrihment Material in Senior High Shool, International onferene on Advanes in Eduation Tehnology, Pulished y Atlantis Press, [7] Mullen, J.G., Ronald., dan ouis B (1978) : On optimizing an Arhiald ruerand heat engine, Amerian Journal of Physis, 46, [8] Stong,. (1971) : The Amateur Sientist, Sientifi Amerian, 4(4), [9] Zemansky, M. dan R. H. Dittman, Heat and Thermodynamis, 7 th ed., Singapore: MGraw Hill, [10] Pellier, J., J. A. Manzanares, dan S. Mafe (1997) : Ideal systems in lassial thermodynamis, Eur. J. Phys, 18, [11] Talanquer, V (004) : Relaiming the entral role of equations of state in thermodynamis, J. hemial Eduation, Aepted 11/04. [1] Galperin, Y (004) : Prolems for the ourse statistial physis, pp