Calculation method and application of specific heat capacity of mixed solids
Specific heat capacity tester
Specific heat capacity is the amount of heat required to raise a unit temperature per unit mass of a substance. The unit in the International System of Units is Joules per kilogram Celsius (J / (kg·K) or J / (kg·°C), J is Joule, K is the thermodynamic temperature scale, equal to Celsius °C), that is, 1 kg The energy required to raise (or fall) the temperature of 1 degree Celsius. According to this theorem, the most basic formula can be used to:
c=ΔE/mΔT (T-T-T) (C=Q/m⊿t in middle school textbook)
ΔE is the absorbed heat, Q in the textbook of middle school; m is the mass of the object, ⊿T is the rising (decreasing) value of the temperature after the endothermic (exothermic), and ΔT is written as Δt in the textbook of junior high school. In fact, this is very Non-standard (usually used in our life °C as a unit of temperature, rarely used K, and ΔT = Δt so use ⊿t in the middle school, but the international or higher scientific field, still use ⊿T).
The specific heat capacity of a substance is related to the process being carried out. Commonly used in engineering applications are constant pressure specific heat capacity Cp, constant volume specific heat capacity Cv and saturated state specific heat capacity.
Constant pressure specific heat capacity Cp: is the energy absorbed or released by a unit mass of material under the condition of constant pressure, temperature rise or drop of 1 ° C or 1K.
Constant volume heat capacity Cv: The unit mass of material is increased or decreased by 1 ° C or 1K internal energy absorbed or released under the condition of constant volume (volume).
Saturated state specific heat capacity: is the amount of heat absorbed or released by a unit mass of material in a saturated state when the temperature rises or falls by 1 ° C or 1 K.
unit
The unit of specific heat capacity is a composite unit.
In the international system of units, the main unit of energy, work, and heat is unified into joules. The main unit of temperature is Kelvin, so the international unit of specific heat capacity is J/(kg·K), which is read as "focus [ear] per kilogram [ Ervin]". (The word in [] can be omitted.)
Commonly used units: J/(kg·°C), J/(g·°C), kJ/(kg·°C), cal/(kg·°C), kcal/(kg·°C), and the like. Note that Celsius and Kelvin differ only in the temperature scale representation, and are equivalent in the sense of the magnitude of the temperature difference, so °C and K in these units can be interchanged arbitrarily. For example, "Coke per kilogram Celsius" and "Coke per kilogram open" are equivalent.
Specific heat capacity indicates the physical quantity of the object's ability to absorb heat (or heat)
Calculation
There is an object of mass m, and when the heat ΔQ is absorbed (or released) in a certain process, the temperature rises (or decreases) ΔT, then ΔQ/ΔT is called the heat capacity of the object in the process (referred to as heat capacity). Expressed by C, ie C = ΔQ / ΔT. Dividing the heat capacity by the mass, that is, the specific heat capacity c=C/m=ΔQ/mΔT. For the heat capacity and specific heat capacity of the micro process, there are C=dQ/dT and c=1/m*dQ/dT, respectively. Therefore, in the finite process in which the temperature of the object changes from T1 to T2, the heat absorbed (or released) Q = ∫ (T2, T1) CdT = m ∫ (T2, T1) cdT.
In general, the heat capacity and the specific heat capacity are both functions of temperature, but when the temperature change range is not too large, it can be approximated as a constant. Then there is Q = C(T2-T1) = mc(T2-T1). If the temperature change amount ΔT = T2 - T1, then Q = cm ΔT. This is the basic formula for calculating calories in secondary schools using specific heat capacity.
In English, the specific heat capacity is called: Specific Heat Capacity (SHC).
The formula for calculating thermal energy with specific heat capacity is: Energy=Mass×Specific Heat Capacity×Temperature change
It can be abbreviated as: Energy=SHC×Mass×Temp Ch, Q=cmΔT.
The heat calculation formula related to specific heat: Q=cmΔT, ie Q absorption (release)=cm (T-T-end) where c is specific heat, m is mass, and Q is energy heat. When the heat is absorbed, it is Q=cmΔT liter (subtracting the initial temperature of the object with the actual elevated temperature), and Q=cmΔT is decreased when the heat is released (the temperature after the actual initial temperature is reduced). Or Q=cmΔT=cm (T-T-T), when Q>0, it is endothermic, and when Q<0, it is exothermic.
(The heat calculation involved in the change of the physical state cannot directly use Q=cmΔT, because the specific heat capacity of different substances is generally different, and the specific heat capacity of the substance changes after the change of the physical state occurs.)
Fold edit this paragraph history
Originally in the 18th century, Scottish physicist and chemist J. Black discovered the difference in the amount of heat required to rise to the same temperature for different substances of the same mass, and proposed the concept of specific heat capacity. Almost any substance can measure specific heat capacity, such as chemical elements, compounds, alloys, solutions, and composites.
Historically, heat has been defined by the specific heat of water, and the amount of heat required to raise 1 gram of water by one degree is defined as 1 calorie.
Specific heat capacity of the mixture
Weighted average calculation:
c=ΣC/ΣM=(m1c1+m2c2+m3c3+...)/(m1+m2+m3+...).
Specific heat capacity of gas
definition:
Cp constant pressure specific heat capacity: the pressure constant, the heat capacity when the temperature changes with volume, Cp = dH / dT, H is ç„“.
Cv constant volume specific heat capacity: the volume is constant, the heat capacity when the temperature changes with pressure, Cv=dU/dT, U is internal energy.
Then, when the gas temperature is T and the pressure is P, the specific heat capacity of the gas when the heat dQ is provided:
Cp*m*dT=Cv*m*dT+PdV;
Where dT is the amount of temperature change and dV is the amount of volume change.
Specific heat capacity of an ideal gas:
The constant volume specific heat capacity and molar specific heat capacity for a gas with f degrees of freedom are:
Cv,m=R*f/2
Cv=Rs*f/2
R=8.314J/(mol·K)
Meyer formula: Cp=Cv+R
Specific heat capacity ratio: γ=Cp/Cv
Multi-specific heat capacity: Cn=Cv-R/(n-1)=Cv*(γ-n)/(1-n)
For both solids and liquids, the specific heat capacity can be measured by the specific pressure heat capacity Cp, ie: C = Cp (measured by the defined method C = dQ / mdT).
Dulong-Petit law:
There is a simple rule for the specific heat capacity of a metal, that is, all metals have a fixed molar heat capacity within a certain temperature range:
Cp≈25J/(mol·K)
and so
Cp=25/M,
Where M is the molar mass and the specific heat capacity unit is J/(kg·K).
Note: The relationship no longer holds when the temperature is much lower than 200K, because C will also tend to 0 for T to 0.
application
The specific heat capacity of water is large, and it has a wide range of applications in industrial and agricultural production and daily life. This application mainly considers two aspects. The first is that a certain amount of water absorbs (or emits) a lot of heat and its temperature does not change much, which is conducive to regulating the climate. The second is that a certain amount of water rises (or decreases). A certain temperature absorbs a lot of heat (or exotherm), which is good for water as a coolant or heating.
First, adjust the climate
The specific heat capacity of water is large and has a significant impact on climate change. In the case of the same heat or cooling, the temperature change of water is smaller. This characteristic of water has a great impact on the climate. During the daytime, the coastal area is slower than the inland area, and the coastal temperature is reduced at night. The change is small, and the inland temperature changes greatly. During the year, the inland is hotter than the coastal in summer, and the winter inland is colder than the coastal. The cause of the formation of sea and land breeze is similar.
1. Impact on temperature
According to Xinhua News Agency, after the impoundment of the Three Gorges Reservoir, the world's largest artificial lake will become a natural "air conditioner", making the climate of the mountain city Chongqing warm in winter and cool in summer. It is estimated that summer temperatures may drop by 5 ° C, and winter temperatures may rise by 3 to 4 ° C.
2. Mitigation of the heat island effect
On a clear, windless summer day, the surface temperature on the island is higher than the surrounding sea temperature, and thus the formation of a sea breeze circulation and cumulus convection over the island is a manifestation of the ocean heat island effect. In recent years, due to the concentration of urban population, industrial development, traffic congestion, and serious air pollution, most of the buildings in the city are built of stone and concrete. In the spatial distribution of temperature, the city is like a warm island, thus forming an urban heat island effect. In terms of mitigating the heat island effect, experts estimate that after a medium-sized urban green belt seedling grows into a thick shade, the green belt has a water source equivalent to a medium-sized reservoir with a volume of 1.14×10m. Because of the large specific heat capacity of the water, it can make the urban summer. The high temperature drops by more than 1 °C, effectively alleviating the increasingly serious "heat island effect".
The establishment of the reservoir, the increase of water, and the specific heat capacity of the water, the temperature change is small when the same cold and heat, so that the summer temperature will not rise higher than in the past, the winter temperature will not fall lower than in the past, so that The temperature remains relatively stable, so the reservoir becomes a huge "natural air conditioner".
Second, cooling or heating
1. Application of water cooling system
People started using water to cool the heat machine very early. In the heat dissipation of the computer CPU, the heat sink can be used to contact the CPU core, so that the heat generated by the CPU is transferred to the heat sink by heat conduction, and then the heat radiated to the air by the fan is used. take away. However, the specific heat capacity of water is much larger than that of air. Therefore, water can be used instead of air as a heat dissipating medium, and the water with increased internal energy can be taken away by a water pump to form a water cooling system. In this way, the temperature of the water generated by the CPU is not significantly increased after the heat is transferred to the water, and the heat dissipation performance is superior to the above system using the air and the fan directly.
The cooling system of a heat engine (for example, an engine of a car, a generator of a power plant, etc.) also uses water as a coolant, and also utilizes the characteristic that the specific heat capacity of seawater is large.
2. Application in agricultural production
Rice is a thermophilic crop. When raising seedlings in March and April every year, in order to prevent frost, farmers generally adopt the method of “shallow water irrigationâ€, that is, water is poured in the fields in the evening, and when the sun rises the next day, Let the water in the field be released. According to the characteristics of the specific heat capacity of water, when the temperature is lowered at night, the temperature of the seedlings is not changed much, and the seedlings are kept warm.
3. Hot water heating
Radiator and warm water bag for heating in winter.
4. Other
For example, in the hot summer, the ancient royal family sheds water from the roof and acts as a heatstroke prevention and cooling function. Hawaii is an island deep in the Pacific Ocean. It has a pleasant climate and is a holy place for tourism and vacation. In addition to the attractive scenery, there is also a major The reason is that it is warm in winter and cool in summer.
For other information, see the term constant pressure specific heat capacity, constant volume specific heat capacity.
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