Anti-freezing floating device and method for preparing phase change solution

Abstract

The application provides an anti-freezing floating device and a preparation method of a phase change solution, relates to the technical field of reservoir anti-freezing, and is used for guaranteeing the safety and reliability of a reservoir in cold weather. The anti-freezing floating device comprises a plurality of floating bodies, a solar heat absorption coating and a plurality of telescopic connecting pieces. The plurality of floating bodies are spaced apart and float on a water body. The floating body has a first containing space and a second containing space. The first containing space is filled with the phase change solution, and the second containing space is filled with gas. The solar heat absorption coating is arranged on the outer surface of the floating body. The plurality of telescopic connecting pieces are arranged at intervals around the reservoir. One end of the telescopic connecting piece is connected with the reservoir, and the other end is connected with the floating body. In this way, the phase change solution can be phase-changed by the ice body extruding the floating body, heat can be released, and the ice body around the floating body can be melted, so that the safety and reliability of the reservoir in cold weather can be guaranteed.

Description

Technical Field

[0001] This application relates to the field of reservoir antifreeze technology, and in particular to an antifreeze floating device and a method for preparing a phase change solution. Background Technology

[0002] Reservoirs in high-altitude and cold regions are prone to freezing. Freezing at the reservoir perimeter where the seepage prevention structure comes into contact with the reservoir can cause freeze-thaw damage or performance aging of the structure, such as asphalt concrete panels, reinforced concrete panels, and geomembranes. Water level fluctuations causing ice blocks to collide with the reservoir banks can physically damage the seepage prevention structure, potentially leading to its failure and leakage. Furthermore, ice sheets, icicles, and ice blocks in the reservoir can also affect the normal operation of generating units or threaten their safety. Summary of the Invention

[0003] To address the aforementioned technical problems, this application provides an antifreeze flotation device and a method for preparing a phase change solution, which are used to ensure the safety and reliability of reservoir operation in cold weather.

[0004] On one hand, this application provides an antifreeze floating device applied around a reservoir. The antifreeze floating device includes multiple floats, a solar heat-absorbing coating, and multiple retractable connectors. The multiple floats float at intervals on the water surface. Each float has a first containment space and a second containment space. The first containment space is filled with a phase change solution, and the second containment space is filled with gas. The solar heat-absorbing coating is applied to the outer surface of the floats. The multiple retractable connectors are spaced at intervals around the reservoir, with one end connected to the reservoir and the other end connected to the float.

[0005] According to the embodiments of this application, the antifreeze floating device fills a phase change solution in the first accommodating space of the float and a gas in the second accommodating space, and applies a solar coating to the outer surface of the float. When the water in the reservoir freezes, the phase change solution undergoes a phase change due to the pressure of the ice, releasing heat and melting the ice around the float. This avoids problems such as damage to the reservoir's perimeter seepage prevention structure and threats to the safe operation of the reservoir's machinery caused by cold weather, thus ensuring the safety and reliability of the reservoir's operation in cold weather. Furthermore, the entire antifreeze process requires no manual operation, reducing the cost of using the antifreeze floating device. Since the solar heat-absorbing coating can absorb solar radiation during the day, it can heat the phase change solution in the first accommodating space. After the float undergoes a phase change and releases heat under pressure, it can recover to or approach its pre-heat-release phase state, preparing it for subsequent phase changes under ice pressure, enabling the reusability of the antifreeze floating device. In addition, the connection between the float and the retractable connector restricts the movement of the float and ensures that the float can change with the water level.

[0006] In one possible implementation, the antifreeze floating device also includes multiple fixing members spaced apart around the perimeter of the reservoir, with one end of the telescopic connector detachably connected to the fixing member and the other end connected to the float.

[0007] In one possible implementation, the antifreeze flotation device also includes a connecting hook, with the float having a connecting hole, and the connecting hook connecting the connecting holes of two adjacent floats.

[0008] In one possible implementation, the retractable connector is detachably connected to the float.

[0009] In one possible implementation, the retractable connector includes a rope, an elastic element, and a fixed hook connected in sequence, with one end of the rope connected to a reservoir and the other end connected to the elastic element, and the fixed hook connected to the connecting hook.

[0010] In one possible implementation, the float has a first surface, which is the surface of the float that is exposed in the water, and a solar heat-absorbing coating is disposed on the first surface.

[0011] In one possible implementation, the float is spherical and the first containment space is annular.

[0012] In one possible implementation, the float is prism-shaped, and the first containment space divides the second containment space into a first containment subspace and a second containment subspace.

[0013] In one possible implementation, the volume of the gas in the second containment space and the volume of the phase change solution in the first containment space satisfy the following formula: V1 / V2=(2ρ2-ρ3) / (ρ3-2ρ1); where V1 is the volume of the gas in the second containment space, V2 is the volume of the phase change solution in the first containment space, ρ1 is the density of the gas in the second containment space, ρ2 is the density of the phase change solution in the first containment space, and ρ3 is the density of the water in the reservoir.

[0014] Secondly, embodiments of this application provide a method for preparing a phase change solution. The preparation method is applied to the aforementioned phase change solution, which is a sodium acetate solution. The preparation method includes the following steps: obtaining the highest temperature T1 reached by the phase change solution after heating with a solar heat-absorbing coating; weighing sodium acetate according to the mass of sodium acetate required for the saturated solution corresponding to the highest temperature T1; adding pure water and mixing thoroughly, then heating to a first temperature T2 to obtain the phase change solution; wherein, the first temperature T2 ≥ the highest temperature T1.

[0015] The technical effects of any design method in the second aspect can be found in the technical effects of different design methods in the first aspect, and will not be repeated here. Attached Figure Description

[0016] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0017] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, those skilled in the art can obtain other drawings based on these drawings without creative effort.

[0018] Figure 1 A schematic diagram showing the connection between the antifreeze floating device provided in some embodiments of this application and a reservoir;

[0019] Figure 2 Schematic diagram of an antifreeze flotation device provided in some embodiments of this application;

[0020] Figure 3 Schematic diagram of a buoy provided for some embodiments of this application;

[0021] Figure 4 Cross-sectional views of the float provided in some embodiments of this application;

[0022] Figure 5 for Figure 4 Sectional view at point A in the middle;

[0023] Figure 6 Cross-sectional views of the float provided in some embodiments of this application;

[0024] Figure 7 for Figure 6 Sectional view at point B;

[0025] Figure 8 This is a graph showing the change in sodium acetate solubility with temperature.

[0026] Figure label:

[0027] 100. Antifreeze floating device; 200. Reservoir; 201. Seepage-proof structure; 202. Ice body;

[0028] 1. Float; 11. First containment space; 111. Phase change solution; 12. Second containment space; 121. Gas; 13. Connecting hole;

[0029] 2. Telescopic connectors;

[0030] 3. Fasteners;

[0031] 4. Connect the hook. Detailed Implementation

[0032] To better understand the above-mentioned objectives, features, and advantages of this application, the solution of this application will be further described below. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0033] In the description of this invention, it should be understood that the terms "upper", "lower", "front", "rear", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0034] In the description of the embodiments of this application, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, "linking" can be a detachable connection or a non-detachable connection; it can be a direct connection or an indirect connection through an intermediate medium. "Fixed connection" refers to a connection where the relative positional relationship remains unchanged after the connection. Furthermore, the directional terms mentioned in the embodiments of this application, such as "inner" and "outer," are only for reference to the directions in the accompanying drawings. Therefore, the directional terms used are for better and clearer explanation and understanding of the embodiments of this application, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of this application.

[0035] In the description of embodiments of this application, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0036] Please see Figure 1 and Figure 2 , Figure 1 This is a schematic diagram showing the connection between the antifreeze floating device provided in some embodiments of this application and a reservoir. Figure 2This is a schematic diagram of an antifreeze floating device provided in some embodiments of this application. An embodiment of this application provides an antifreeze floating device 100, applied to the perimeter of a reservoir 200. The antifreeze floating device 100 may include multiple floats 1, a solar heat-absorbing coating, and multiple retractable connectors 2.

[0037] Multiple floats 1 are spaced apart and float on the water surface. Specifically, multiple floats 1 are set in the water body of reservoir 200, and there is a gap between two adjacent floats 1. Here, "floating" means that part of the float 1 is located in the water body, and the rest of the float 1 may be located outside the water body.

[0038] The float 1 may have a first accommodating space 11 and a second accommodating space 12. The first accommodating space 11 and the second accommodating space 12 are independent spaces.

[0039] The first containment space 11 can be filled with a phase change solution 111. Therefore, when the water in the reservoir 200 freezes, the ice 202 will compress the float 1, causing the first containment space 11 to also be compressed. This allows the phase change solution 111 to undergo a phase change, releasing heat and melting the ice 202 around the float 1. This helps prevent damage to the reservoir's perimeter seepage prevention structure 201 and ensures safe operation of the system, thus guaranteeing the safety and reliability of the reservoir 200 in cold weather. Furthermore, the entire antifreeze process requires no manual operation, thereby reducing the operating cost of the antifreeze floating device 100.

[0040] For example, the first containing space 11 may have an opening communicating with the outside, and the opening may be equipped with a sealing cap. The phase change solution 111 in the first containing space 11 can be replaced through the opening, thereby improving the service life of the antifreeze flotation device 100 and reducing the user's operating costs.

[0041] The second containment space 12 can be filled with gas 121. Specifically, the gas 121 filled in the second containment space 12 can be air, hydrogen, etc. By filling the second containment space 12 with gas 121, the buoyancy of the float 1 can be adjusted. Furthermore, since the structure for adjusting the buoyancy of the float 1 is simple, it is beneficial to reduce the manufacturing cost of the float 1, which in turn helps to reduce the manufacturing cost of the antifreeze flotation device 100.

[0042] For example, the second containment space 12 may have an air inlet, through which the gas 121 in the second containment space 12 can be replaced or replenished.

[0043] It should be noted that the material of the float 1 can be a flexible material, which gives the float 1 good elasticity and load-bearing capacity, and allows the float 1 to hold more gas 121, thereby facilitating the adjustment of the float 1's buoyancy.

[0044] A solar-heat-absorbing coating can be applied to the outer surface of the float 1. This coating effectively absorbs solar radiation during the day, converting light energy into heat energy which is stored in the phase change solution 111. This heats the phase change solution 111 within the first containment space 11, allowing it to recover to or near its pre-heat-release phase state after undergoing a phase change under pressure. This prepares the float for subsequent phase change under ice pressure, enabling the reusability of the antifreeze floatation device 100. Furthermore, the solar-heat-absorbing coating is environmentally friendly, pollution-free, and sustainable, thus improving the environmental friendliness of the antifreeze floatation device 100.

[0045] For example, the solar heat-absorbing coating can be aluminum nitride, aluminum oxide, titanium dioxide, silicon dioxide, or other novel coating materials.

[0046] Multiple retractable connectors 2 are spaced apart around the perimeter of the reservoir 200. One end of each retractable connector 2 is connected to the reservoir 200, and the other end is connected to the float 1. Specifically, one end of the retractable connector 2 is fixedly connected to the reservoir 200, and the other end can extend to the water level and connect to the float 1. Since the retractable connector 2 can be compressed or extended, when the water level rises or falls, the compression or extension of the retractable connector 2 can ensure that the float 1 floats on the water, while also restricting the float 1 from floating near the perimeter of the reservoir 200.

[0047] According to the embodiment of this application, the antifreeze floating device 100 fills the first accommodating space 11 of the float 1 with a phase change solution 111, fills the second accommodating space 12 with gas 121, and applies a solar energy coating to the outer surface of the float 1. When the water in the reservoir 200 freezes, the ice 202 compresses the float 1, causing the phase change solution 111 to undergo a phase change, releasing heat and melting the ice 202 around the float 1. This avoids problems such as damage to the reservoir's perimeter seepage prevention structure 201 and threats to the safe operation of the reservoir 200 caused by cold weather, thus ensuring the safety and reliability of the reservoir 200 under cold weather conditions. Furthermore, the entire antifreeze process requires no manual operation, thereby reducing the operating cost of the antifreeze floating device 100. Furthermore, since the solar-absorbing coating can absorb solar radiation during the day, it can heat the phase change solution 111 in the first containment space 11. After the float 1 is compressed and undergoes a phase change to release heat, it can recover to or approach the phase state before releasing heat. This prepares it for subsequent compression by the ice body 202 to undergo a phase change, enabling the reusability of the antifreeze floating device 100. In addition, the connection between the float 1 and the retractable connector 2 can restrict the movement of the float 1 and ensure that the float 1 can change with the water level.

[0048] Please continue reading. Figure 1 and Figure 2 In some embodiments, the float 1 may have a first surface. The first surface is the surface of the float 1 that is exposed above the water, and the solar heat-absorbing coating is disposed on the first surface. This arrangement allows the solar heat-absorbing coating to be disposed only on the first surface of the float 1, thereby helping to reduce the manufacturing cost of the antifreeze floating device 100. At the same time, it also ensures that the solar heat-absorbing coating can better absorb solar energy.

[0049] Please continue reading. Figure 1 and Figure 2 In some embodiments, the antifreeze floating device 100 may further include multiple fixing members 3. The multiple fixing members 3 are spaced apart around the perimeter of the reservoir 200. One end of the telescopic connector 2 is detachably connected to the fixing member 3, and the other end is connected to the float 1. Specifically, the multiple fixing members 3 can be spaced apart around the perimeter of the reservoir 200, and parts of the fixing members 3 can be inserted into the bank slope of the reservoir 200. The fixing members 3 are connected to the float 1 through the telescopic connector 2. By setting the fixing members 3, the position of the float 1 can be limited, and the replacement and maintenance of the telescopic connector 2 can be facilitated, which helps to improve the service life of the antifreeze floating device 100.

[0050] For example, fastener 3 can be an anchor bolt.

[0051] Please see Figure 2 and Figure 3 , Figure 3This is a schematic diagram of a float provided in some embodiments of this application. In some embodiments, the antifreeze floating device 100 may further include a connecting hook 4. The float 1 may have a connecting hole 13. The connecting hook 4 connects to the connecting holes 13 of two adjacent floats 1. Specifically, each of the two adjacent floats 1 has a connecting hole 13, and the two connecting holes 13 are opposite each other. One end of the connecting hook 4 can be connected to the connecting hole 13 of one float 1, and the other end can be connected to the connecting hole 13 of the other float 1. Thus, multiple floats 1 can be connected in series by the connecting hook 4. The connection between multiple floats 1 is detachable, which facilitates the replacement of a single damaged float 1, thereby improving the maintainability of the antifreeze floating device 100.

[0052] For example, one side of the float 1 may have a protrusion, and the connecting hole 13 may be formed on the protrusion. This arrangement facilitates the connection of multiple floats 1, thereby reducing the assembly difficulty of the antifreeze floating device 100.

[0053] Please continue reading. Figure 2 and Figure 3 In some embodiments, the retractable connector 2 is detachably connected to the float 1. This facilitates the replacement and maintenance of the float 1 or the retractable connector 2, thereby improving the maintainability of the antifreeze flotation device 100.

[0054] Please continue reading. Figure 2 and Figure 3 In some embodiments, the retractable connector 2 may include a rope, an elastic element, and a fixed hook connected in sequence. One end of the rope is connected to the reservoir 200, and the other end is connected to the elastic element. The fixed hook is connected to the connecting hook 4. Specifically, one end of the rope is connected to the reservoir 200, and the other end is connected to the elastic element. The elastic element is connected to the fixed hook, and the fixed hook is connected to the connecting hook 4. Thus, when the water level rises or falls, the float 1 can cause the elastic element to compress or extend through the rope, thereby realizing the automatic extension and retraction of the retractable connector 2. The structure is simple and helps to reduce the manufacturing cost of the anti-freeze floating device 100.

[0055] For example, the elastic element can be a spring.

[0056] Please see Figure 4 and Figure 5 , Figure 4 Cross-sectional views of the float provided in some embodiments of this application. Figure 5 for Figure 4A cross-sectional view at point A. In some embodiments, the float 1 is spherical in shape, and the first receiving space 11 is annular in shape. Specifically, the first receiving space 11 abuts against the side wall of the float 1, so that the first receiving space 11 and the float 1 have a larger contact area. The middle area of ​​the annular shape is the second receiving space 12. This arrangement allows the float 1 to have a larger receiving space, and facilitates the absorption of heat transferred by the solar heat-absorbing coating by the first receiving space 11. It also facilitates the transfer of heat to the ice body 202 during phase change, which can reduce heat loss during heat transfer.

[0057] Please see Figure 6 and Figure 7 , Figure 6 Cross-sectional views of the float provided in some embodiments of this application. Figure 7 for Figure 6 A cross-sectional view at point B. In some embodiments, the float 1 is prism-shaped, and the first receiving space 11 divides the second receiving space 12 into a first receiving subspace and a second receiving subspace. This arrangement simplifies the structure, helps reduce the manufacturing cost of the float 1, and also facilitates the control of the mass of the gas 121 and the phase change solution 111.

[0058] It should be noted that the water level is located in the middle of the first containment space 11. This facilitates the transfer of heat during phase change.

[0059] Please continue reading. Figures 4-7 In some embodiments, the volume of gas 121 in the second containment space 12 and the volume of phase change solution 111 in the first containment space 11 satisfy the following formula:

[0060] V1 / V2=(2ρ2-ρ3) / (ρ3-2ρ1);

[0061] Wherein, V1 is the volume of gas 121 in the second containment space 12, V2 is the volume of phase change solution 111 in the first containment space 11, ρ1 is the density of gas 121 in the second containment space 12, ρ2 is the density of phase change solution 111 in the first containment space 11, and ρ3 is the density of water in reservoir 200.

[0062] Therefore, by adjusting the relative position and density of the first accommodating space 11 and the second accommodating space 12, the float 1 can float on the water surface, and the water surface line can be located in the middle of the first accommodating space 11.

[0063] For example, when phase change solution 111 is a saturated sodium acetate solution at 40°C, ρ2 = 1.14 g / cm³. 3 ρ3=1g / cm 3 Gas 121 uses air, ρ1 = 1.29 × 10 -3 g / cm 3Therefore, the ratio of V1 / V2 is approximately 1.28.

[0064] This application provides a method for preparing a phase change solution 111. The preparation method is applied to the aforementioned phase change solution 111, which is a sodium acetate solution. The main components of the sodium acetate solution are CH3COONa and H2O. The preparation method may include the following steps:

[0065] The highest temperature T1 reached by the phase change solution 111 after heating with the solar heat-absorbing coating is obtained. Specifically, the highest temperature T1 is related to the heat absorption efficiency of the solar heat-absorbing coating on the surface of the float 1, which can be determined experimentally. The float 1 coated with the solar heat-absorbing coating can be exposed to sunlight or simulated sunlight for N hours (N is the local average number of hours of sunlight) and the highest temperature T1 that the phase change solution 111 inside the float 1 can reach is measured.

[0066] Weigh out the sodium acetate according to the required mass of sodium acetate for the saturated solution corresponding to the highest temperature T1. Specifically, refer to Table 1 or... Figure 8 Sodium acetate is weighed based on the change in solubility of sodium acetate with temperature.

[0067] Table 1 Solubility of Sodium Acetate

[0068] Temperature ℃ 0 10 20 30 40 60 80 90 100 Solubility (g) 36.2 40.8 46.4 54.6 65.6 139 153 161 170

[0069] After adding pure water and mixing thoroughly, heat to the first temperature T2 to obtain phase change solution 111;

[0070] Wherein, the first temperature T2 is greater than or equal to the highest temperature T1.

[0071] For example, after being exposed to sunlight, the highest temperature T1 of the phase change liquid inside float 1 is 40℃. Therefore, a phase change solution 111 is prepared by using at least 65.6g of sodium acetate per 100g of water. This ensures that the solution is saturated or unsaturated when the temperature is greater than or equal to 40℃, and supersaturated when the temperature is less than 40℃. This allows the solution inside float 1 to be supersaturated when the outside temperature drops to 0℃ or below. When ice forms on the surface of reservoir 200 and compresses float 1, the phase change solution 111 is easily disturbed, undergoing a phase change and releasing heat to melt the surrounding ice. During the day, the solar-heat-absorbing coating on float 1 absorbs solar radiation, causing the internal solution temperature to rise back to 40℃, and the solution gradually returns to a saturated or unsaturated state, preparing for the next phase change to release heat and melt the ice.

[0072] In the description of this specification, specific features, structures, materials, or characteristics may be combined in any suitable manner in one or more embodiments or examples.

[0073] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A frost-resistant floating device, applied around the perimeter of a reservoir, characterized in that, The antifreeze flotation device includes: Multiple floats are spaced apart and float on the water. Each float has a first containment space and a second containment space. The first containment space is filled with a phase change solution, and the second containment space is filled with gas. A solar heat-absorbing coating is disposed on the outer surface of the float; Multiple retractable connectors are spaced apart around the perimeter of the reservoir. One end of each retractable connector is connected to the reservoir, and the other end is connected to the floating body. The volume of the gas in the second containment space and the volume of the phase change solution in the first containment space satisfy the following formula: V1 / V2=(2ρ2-ρ3) / (ρ3-2ρ1); Wherein, V1 is the volume of the gas in the second containment space, V2 is the volume of the phase change solution in the first containment space, ρ1 is the density of the gas in the second containment space, ρ2 is the density of the phase change solution in the first containment space, and ρ3 is the density of the water in the reservoir.

2. The antifreeze floating device according to claim 1, characterized in that, The antifreeze floating device also includes multiple fixing components, which are spaced apart around the perimeter of the reservoir. One end of the telescopic connector is detachably connected to the fixing component, and the other end is connected to the float.

3. The antifreeze floating device according to claim 1, characterized in that, The antifreeze floating device also includes a connecting hook, and the float has a connecting hole, and the connecting hook connects the connecting holes of two adjacent floats.

4. The antifreeze floating device according to claim 3, characterized in that, The retractable connector is detachably connected to the float.

5. The antifreeze floating device according to claim 4, characterized in that, The retractable connector includes a rope, an elastic element, and a fixed hook connected in sequence. One end of the rope is connected to the reservoir, and the other end is connected to the elastic element. The fixed hook is connected to the connecting hook.

6. The antifreeze floating device according to claim 1, characterized in that, The float has a first surface, which is the surface of the float that is exposed in the water, and the solar heat-absorbing coating is disposed on the first surface.

7. The antifreeze floating device according to claim 1, characterized in that, The float is spherical in shape, and the first accommodating space is annular in shape.

8. The antifreeze floating device according to claim 1, characterized in that, The float is prism in shape, and the first accommodating space divides the second accommodating space into a first accommodating subspace and a second accommodating subspace.

9. The antifreeze floating device according to claim 1, characterized in that, The phase change solution is a sodium acetate solution, and the preparation method includes the following steps: The highest temperature T1 reached by the phase change solution after heating by the solar heat-absorbing coating was obtained; Weigh out the sodium acetate according to the mass of sodium acetate required for the saturated solution corresponding to the highest temperature T1. After adding pure water and mixing thoroughly, heat to the first temperature T2 to obtain a phase change solution; Wherein, the first temperature T2 is greater than or equal to the highest temperature T1.

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