Bimetallic strip worksheet answers

Continue The bimetallic strip consists of two different materials with different expansion ratios that are related to each other. For example, for brass and steel, linear expansion ratios: brass: 19 x 10-6/C steel: 11 x 10-6/C When this bimetallic band is heated, brass expands more than steel and strip curves with brass on the outside. If the band is cooled, it curves with steel on the outside. Bimetallic strips are used as switches in . and zinc strips are the same length of 20 cm at 20 degrees Celsius (a) What will be the difference in the length of the strips at 100 degrees Celsius? b) The stripes were chained to each other at 20 degrees Celsius and formed the so-called bimetallic strip. Suppose it bends into an arc when heated. Determine which metal will be on the outside of the arc and what will be the arc radius at 100 degrees Celsius. The thickness of each band is 1 mm. t0 - 20 degrees Celsius, in which both strips are equally long l0 and 20 cm, the length of both bands is 0.20 m at t0 t. difference in length of both bands at t d 1 mm and thickness of 1'10-3 m of each band r ? The radius of the curved bimetallic strip From tables No 30-10- 6K-1 ratio of linear thermal zinc expansion NoCu 17'10-6K-1 ratio of linear of copper substances expands when we raise their temperature. Different substances expand in different ways, so there will be a difference in the length of the two bands. As long as the strips are firmly chained to each other so that they can't move along each other, they will bend. A band that expands less will be on the inside, so in our case it will be copper. Because the thickness of the stripes is constant, the two curves differ in length. The difference in the length of both arcs should correspond to the difference in length caused by the different thermal expansion of the two metals. First, we express the length of both strips at temperature t. \[l_{Cu}=l_0\,(1+\alpha_{Cu}\Delta t)\] \[l_{Zn}=l_0\,(1+\alpha_{Zn}\Delta t)\] We subtract one length from another: \[\Delta l=l_{Zn}-l_{Cu}\] \[\Delta l=l_0\,(1+\alpha_{Zn}\Delta t)-l_0\,(1+\alpha_{Cu}\Delta t)\] \[\Delta l=l_0\,(\alpha_{Zn}-\alpha_{Cu})\Delta t\] \[\Delta l=l_0\,(\alpha_{Zn}-\alpha_{Cu})\,\left(t-t_0\right)\] Finally, we substitute for numerical values: \[\Delta l=l_0\,(\alpha_{Zn}-\alpha_{Cu})\,\left(t-t_0\right)\] \[\Delta l=0.2\cdot\,(30\cdot{10^{-6}}-17\cdot{10^{-6}})\cdot\,\left(100-20\right)\,\mathrm{m}\] \[\Delta l=2.08\cdot{10^{-4}}\ , mathrm'm0.208, mathrmmm, as the strips are firmly attached to each other, they will bend during heating. Consider that the length of the strip corresponding to the increased temperature is in the Strip. We've already expressed the length of both bands partially a), but we can also express this through φ and desired radius r. From there we can determine the radius of r. Note: When the temperature rises, the thickness of the bands also increases. However, this effect has very little effect on the result, so you can ignore it. We will use the image to calculate the radius of the arc. Because the strips are firmly attached to each other, they will bend during heating. Keep in mind that the strip length corresponding to the elevated temperature is in the middle of the strip. The radius of the smaller arc to r. The radius of the larger arc is R: Rfracd_1 d_2 {2}, where d1 and d2 are increased thicknesses of both bands. The length of the circular arc can be defined as the product of the radius and angle of the φ (in the radian). l_ Cur'varphi (l_ n (r'fracd_ n{2}frac d_ Cu{2}) We subtract the length of one arc from another and understand that their difference should be equal to the difference in the length of the bands that we expressed in part a) of the task. Delta ll_n-l_Cu (r'fracd_ n{2}fracd_ Cu{2})varphi-r'varphi'frac{1} {2} (d_ d_ lengths and increased thickness at high temperature l_0 (alpha_ -alpha_ Delta t'frac{1}{2}'d (1alpha_ CuDelta t)d (1'alpha_ 'n'Delta t)l_0 ,alpha_ yen alpha_ Ku{1}{2})Delta t'frak{1}{2}d2 (alpha_ (Kua alpha_)t) : Warfi 2l_o (alpha_)-alpha_ (Kua)) Delta t22 (alpha_ Cualpha_)Delta t) For the length of the heated copper band it corresponds to the reality of l_o (1alpha_ CuDelta t φ) : Frak l_o (1alpha_ Delta t) alpha_ alpha_ 2l_o l_o (1 alpha_ Delta talpha_) alpha_ Delta t) Ryo Frak (alpha_ Ku Delta t) 2 (alpha_ Kue alpha_) Delta etc.2 (Alpha_ ing-alpha_) Delta etc. we replace these values : Frak (117'cdot10'-6'cdot{80})2 (30'cdot-10'-6 17-kdot 10-10-10-2 80'2'cdot (30'cdot-10'-6'-1 7'cdot-10'-6')) mathrm-m'dot)96, mathrmcm: If we look more closely at both expressions in brackets as a result of the faction, it is obvious that we can omit terms that contain heat coefficients No. The first expression in brackets is associated with a change in the length of one band, and the second expression in brackets corresponds to a change in the thickness of the strip. On the contrary, we cannot make any omission of expression brackets in the denominator, because both terms are of similar magnitude. This expression is associated with a difference in the linear expansion of both metals. This will give us a simpler attitude: the dot tailcoats (1 euro...) (2 euros) No 2 (alpha_---Ku alpha_) Delta i.e. d'frak de (alpha_.- alpha_Ku) (Delta- t'10-3' (30'cdot-10'-1-16'-17'c 10-6)) kdot{80}, matrm-dot 0.9615, matemarmamamamamam Difference in the length of two bands will be about 0.2 mm, and the bimetallic band will bend into an arc with a radius of about 96 cm. This article needs additional quotes to verify. Please help improve this article by adding quotes to reliable sources. Non-sources of materials can be challenged and removed. Find sources: Bimetallic stripe - News newspaper book scientist JSTOR (February 2012) (Learn how and when to remove this pattern message) A bimetallic strip diagram showing how the difference in thermal expansion in the two metals leads to a much larger lateral shift of the strip of the bimetallic coil from the reacts to the heat from the lighter, by unwinding and then the backup. The bimetallic band is used to convert temperature changes into mechanical displacement. The band consists of two strips of different metals that expand at different speeds as they heat up, usually steel and copper, and in some cases steel and brass. Different extensions cause the flat band to bend to one side when heated, and in the opposite direction if it cools below the initial temperature. A metal with a higher thermal expansion factor is on the outside of the curve when the band heats up and on the inside when cooled. The invention of the bimetallic band is usually attributed to , an eighteenth-century watchmaker who did so for his third (H3) of 1759 to compensate for temperature changes in the balance sheet in the spring. Harrison's invention is recognized at a memorial to him at Westminster Abbey, England. This effect is used in a number of mechanical and electrical devices. The characteristics of the band consists of two strips of different metals that expand at different speeds as they heat up, usually steel and copper, and in some cases steel and brass. The stripes are connected to each other along their entire length, riveting, rationing or welding. Different extensions cause the flat band to bend to one side when heated, and in the opposite direction if it cools below the initial temperature. A metal with a higher thermal expansion factor is on the outside of the curve when the band heats up and on the inside when cooled. The side-shifting band is much larger than a slight extension of length in either of the two metals. In some apps bimetallic strips are used in a flat form. In others, it is wrapped in a coil for compactness. The long length of the spiral version gives an improved sensitivity. The curvature of the bimetall beam can be described by the following equation: No. 6 E 1 E 2 (h 1 and h 2) h 1 h 2 ε E 1 2 h 1 4 4 4 E 1 E 2 h 1 3 h 2 x 6 E 1 E 2 h 1 1 2 2 2 2 2 h 2 x 4 E 1 E 2 h 2 3 h e E 2 h 2 2 2 4 display kappa Frak (6E_{1}E_{2} h_{1})h_{2}) h_{1}h_{2} Epsilon E_{1} {2}h_{1} {4} 4E_{1}E_{2}h_{1} {3}h_{2} 6E_{1}E_{2}h_{1} {2}h_{2} {2} 4E_{1}E_{2}h_{2}-{3}h_{1}-E_{2}-{2}h_{2}-{4} where no 1/R display kappa 1/R and R R display is a curvature radius, E 1 displaystyle E_{1} and h 1 displaystyle h_{1} is a module and height (thickness) of material 1 and E 2 displaystyle E_{2} and h 2 displaystyle h_{2} is a module and height (thickness) of two material. ε Epsilon display is a mismatch of the strain calculated by: ε (α 1 - α 2) T displaystyle epsilon (Alpha {1} Alpha Alpha -Alfa -{2}), Delta T, where the No.1 is the ratio of thermal expansion of material one and No.2 is the ratio of thermal expansion of material two. TT is the current temperature minus the reference temperature (the temperature at which the beam has no bending). The conclusion of the curvature radius Main article: Bimetallic stripe - Characteristics Let the layer on the concave side be layer 1, and on the touted side - layer 2, and let the thickness of each of them be h 1 display style h_{1} and h 2 displaystyle h_{2} respectively. Layer 1 is in suspense with force outwards at each end of F1 (display F_{1}), while layer 2 is compressed with force inside at each end of F 2 (display F_{2}). Because the system is in the balance of F 1 and F 2 , F (display F_{1})F_{2} F. At each end of layer 1 there is a bend moment M 1 (display M_{1}), and similar to layer 2. If R -displaystyle R is a curvature radius, then M 1 and E 1 I 1 /R displaystyle M_{1}E_{1}I_{1}/R and M 2 E 2 I 2/ R displaystyle M_{2} E_{2}I_{2}/R, where E displayural EI is Flex rigidity, E display Estyle is a module of Young, and I display is the second point of the area. For a rectangular cross-section of width w 'displaystyle w', I 1 - w h 1 3/12 displaystyle I_{1}wh_{1}{3}/12 and I 2' w h 2 3/12 'displaystyle I_{2} 'wh_{2}'{3}/12. Spouses produced by F (displaystyle F) operating along the middle lines of each layer and separated by h 1/2 h x 2 h/2 h/2 displaystyle h_{1}/2 h_{2}/2'h/2 is F h/2 displaystyle Fh/2, and again because, that the band is in balance and there are no external applied torques, F h / 2 - M 1 - M 2 (display Fh/2'M_{1}) M_{2}. . So F h 2 - w 12 R (E 1 h 1 3 - E 2 h 2 3 {2}) . Now we're looking at the contact surface between the two layers. The length of this surface for layer 1 is L 0 (1 - α 1 (T - T 0) - F 1 / w h 1 E 1 x 1/2 R F_{1}) T_{0} {1} L_{0} . wh_{1}E_{1}-h_{1}/2R) where T 0 (T_{0} display) is the temperature when the band is straight, L 0 (L_{0} display) is the length of the layer when the temperature is T t t 0 (T'T_{0} display) (i.e. when it is straight and stress-free from layer 2), and α 1 alpha {1} display is a thermal expansion factor (fractional length increase per unit of temperature increase). The second term here is clearly a fractional change in length produced by the thermal extension, the third term is the stress caused by stress F 1 / w h 1 displaystyle F_{1}/wh_{1} due to the force of F 1 (display F_{1}) acting over the end area (positive because the force is tense). The last term is the additional length of the contact surface relative to the middle line of layer 1 (positive because the contact surface is an external, emasible surface). Similarly, the length of this surface for layer 2 is L 0 (1 and α 2 (T - T 0) - F 2 / w h 2 E 2 - h 2 /2 L_{0} R). (1-alpha-{2} (T-T_{0})-F_{2}/wh_{2}E_{2}-h_{2}/2R) (minus the signs, because the compression force and contact is on the inside). Since the surfaces are connected, α 1 (T - T 0 ) - F w h 1 E 1 - h 1 2 R - α 2 (T - T 0 ) - F w h 2 E T_{0} {1} 2 frak (F- wh_{1}E_{1}) - {2} h_{1} frak (F-wh_{2}E_{2})T_{0}-frak (h_{2}) . Rebuilding to extract the No. 1/R display style kappa 1/R, collecting terms and eliminating F 'displaystyle F' using the equation above produces an equation for the displaystyle kappa in the main article. Insight can be obtained, If just this result is multiplied from top to bottom on (h 1 h 2) / E 1 E 2 h 1 2 2 display style (h_{1} h_{2}) / E_{1}E_{2}h_{1} {2}h_{2}{2} 1) r E r h 2 4 r h r_ r_ r_ ε 6 and 4 r h Eh r_hha {2} 4r_hha 6 4r_h-1 r_ ez-1 r_hh-2 - Epsilon 1h x 2 (display style h'h_{1}'h_{2}), p h x 1/h 2 display style r_hh_{1}/h_{2} and r e e e 1 / E 2 display r_ EE_{1}/E_{2} Since then (1 x x) (1 x) - 1 ≈ 2 (x 2) (1 x) (1x) - 1 approximately 2O (x'{2}) for small x displaystyle xstyle , which is insensitive to x display x due to lack of terms of first order, then we can zoom in r h and r h 1 ≈ 2 display r_ hr_ h'h'- 1'approx 2 for r h (display) style r_ close to unity (and insensitive to r h 'displaystyle r_ h'), and r E r h 2 r E - 1 r ≈ h r_ «Е-r_хх»{2}»r_ «ЭЗ-1» r_хх-2»приблизительно 2» для r E r h 2 (дисплей) стиль r_ «E»r_'h'{2}» близок к единству (и нечувствительный к r E r h 2 (дисплей r_ »E»r_'h'{2}). Таким образом, если только r h 'displaystyle r_'h' или r E 'displaystyle r_'E' очень далеки от единства, мы можем приблизиться к ≈ 3 ε / 2 ч . История Мемориала Джона Харрисона в Вестминстерском аббатстве, Лондон Самая ранняя сохранившаяся биметаллическая полоса была сделана часовщиком восемнадцатого века Джоном Харрисоном, которому, как правило, приписывают его изобретение. Он сделал это для своего третьего морского хронометра (H3) 1759 года, чтобы компенсировать температурные изменения в балансе весной. Его не следует путать с биметаллическим механизмом коррекции теплового расширения в его гритиронном маятнике. Его ранние примеры имели две отдельные металлические полосы connected by rivets, but he also invented a more masterly technique of direct alloy of molten brass on a steel substrate. A band of this type was installed on its last timekeeper, the H5. Harrison's invention is recognized at a memorial to him at Westminster Abbey, England. This effect is used in a number of mechanical and electrical devices. The watch's mechanical clock mechanisms are sensitive to temperature changes as each part has tiny tolerance and leads to errors in time. To compensate for this phenomenon, a bimetallic band is used in the mechanism of some watches. The most common method is the use of bimetallic design for the circular rim of the . What it does is move the weight in a radial way, looking at the circular plane down the balance of the wheel, changing the momentum of the inertia of the balance of the wheel. As the spring controlling balance becomes weaker with the increasing temperature, the balance becomes smaller in diameter to reduce the moment of inertia and keep the period of oscillations (and hence the timekeeping) constant. Currently, this system is no longer in use since the emergence of low-calorie alloy coefficients such as nivarox, parachrome and many others depending on each brand. thermostats with bimetallic coils on (2) See also: Turning points and popping drive bimetallic thermostats In the regulation of heating and cooling, thermostats that work in a wide range of temperatures are used. In them, one end of the bimetallic band is mechanically fixed and attached to the power source, while the other (moving) end carries an electric contact. In adjustable thermostats, another contact is located with a control handle or lever. The position, so-called, controls the adjustable temperature, called the established point. Some thermostats use a mercury switch connected to both electrical wires. The angle of the entire mechanism is adjustable for management the point of the thermostat. Depending on the application, a higher temperature can open contact (as (as heater) or it can close the contact (as in the refrigerator or air conditioner). Electrical contacts can control power directly (as in household iron) or indirectly, switching electricity through a relay or supplying natural gas or fuel oil through an electrically operated valve. In some gas heaters, power can be provided by a thermococle, which is heated by experimental light (small, continuously burning, flame). In devices without pilot lights for ignition (as in most modern dried gas clothing and some gas heaters and decorative fireplaces) the power for contacts is provided by reducing household electricity, which runs the electronic ignition relay, or resistance heater or electrically powered sparks generating devices. Straight-pointing dial are actually common in daily use devices (such as a patio thermometer or meat thermometer) that uses a bimetallic strip wrapped in a coil in its most commonly used design. The coil changes the linear motion of the metal extension into a circular motion thanks to the lyco-shaped shape it draws. One end of the coil is attached to the body of the device as a fixation point, and the other controls the pointing needle inside the circular indicator. The bimetallic strip is also used in the recording thermometer. The Brege thermometer consists of a three-metal spiral in order to have a more accurate result. Heat engines Heat is not the most efficient, and using bimetallic bands the efficiency of thermal engines is even lower, as there is no camera to contain heat. In addition, bimetallic bands cannot produce strength in their movements, the reason being that to achieve reasonable bends (movements) both metal bands must be thin to make the difference between the expansion noticeable. Thus, the use of metal bands in thermal engines is mainly in simple toys that were built to demonstrate how the principle can be used to drive a thermal engine. (quote is necessary) Bimetal electric strip devices are used in miniature switches to protect circuits from excess current. The wire coil is used to heat the bimetallal strip, which bends and controls the link that disconnects the spring contact. This breaks the chain and can be reset when the bimetallal strip cools down. Bimetallic strips are also used in time-delayed relays, gas furnace safety valves, thermal flashing lights for old turn signal lamps and fluorescent lamps. In some devices, current running directly through bimetallic bands is sufficient for heating and direct contact operation. has also been used in mechanical PWM voltage regulators for automotive use. See also Thermotime Switch Links Article on Balance Wheel Compensation vs. Temperature Change by Hodinkee Magazine Article On Hair Used Clock monochrome magazine Notes and Sobel, Dawa (1995). Longitude. London: Fourth Estate. page 103. ISBN 0-00-721446-4. One of Harrison's inventions, introduced in H-3... Called... bimetallic stripes. Kline, W. Residual loads in surface coatings and their effect on interfacial debonation. Key Engineering Materials (Switzerland). 116-117, page 307-330. 1996 - Tymoshenko, J. Opt. Soc. Am. 11, 233 (1925) - Sobel, Dawa (1995). Longitude. London: Fourth Estate. page 103. ISBN 0-00-721446-4. One of Harrison's inventions, introduced in H-3... Called... bimetallic stripes. - the outer links Video circular bimetallic wire, driven by a small engine with ice water. Access to February 2011. Video of the bimetallic coil powering the engine (among others like Curie, Stirling and Hero) is extracted from the section 1 enrichment bimetallic strip worksheet answers

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