Determine the average heat capacity in the temperature range. Heat capacity is true, average, isochoric and isobaric. Lab Preparation Guidelines
Heat capacity is the ratio of the amount of heat imparted to the system to the temperature increase observed in this case (in the absence of chemical reaction, the transition of a substance from one state of aggregation to another and at A " = 0.)
Heat capacity is usually calculated per 1 g of mass, then it is called specific (J / g * K), or per 1 mol (J / mol * K), then it is called molar.
Distinguish average and true heat capacity.
Middle heat capacity is the heat capacity in the temperature range, i.e. the ratio of the heat imparted to the body to the increment in its temperature by ΔT
True The heat capacity of a body is the ratio of an infinitesimal amount of heat received by the body to the corresponding increase in its temperature.
It is easy to establish a connection between the average and true heat capacity:
substituting the values of Q into the expression for the average heat capacity, we have:
The true heat capacity depends on the nature of the substance, the temperature and the conditions under which the heat transfer to the system occurs.
So, if the system is enclosed in a constant volume, i.e. for isochoric process we have:
If the system expands or contracts while the pressure remains constant, i.e. For isobaric process we have:
But ΔQ V = dU, and ΔQ P = dH, therefore
C V = (∂U/∂T) v , and C P = (∂H/∂T) p
(if one or more variables are held constant while others change, then the derivatives are said to be partial with respect to the changing variable).
Both ratios are valid for any substances and any states of aggregation. To show the relationship between C V and C P, it is necessary to differentiate the expression for the enthalpy H \u003d U + pV /
For an ideal gas pV=nRT
for one mole or
The difference R is the work of the isobaric expansion of 1 mole of an ideal gas as the temperature rises by one unit.
For liquids and solids, due to a small change in volume when heated, С P = С V
Dependence of the thermal effect of a chemical reaction on temperature, Kirchhoff's equations.
Using Hess's law, one can calculate the thermal effect of a reaction at the temperature (usually 298K) at which the standard heats of formation or combustion of all participants in the reaction are measured.
But more often it is necessary to know the thermal effect of a reaction at different temperatures.
Consider the reaction:
ν A A+ν B B= ν C С+ν D D
Let us denote by H the enthalpy of the participant in the reaction per 1 mole. The total change in the enthalpy ΔΗ (T) of the reaction is expressed by the equation:
ΔΗ \u003d (ν C H C + ν D H D) - (ν A H A + ν B H B); va, vb, vc, vd - stoichiometric coefficients. x.r.
If the reaction proceeds at constant pressure, then the change in enthalpy will be equal to the heat effect of the reaction. And if we differentiate this equation with respect to temperature, we get:
Equations for isobaric and isochoric process
And 
called Kirchhoff equations(in differential form). They allow qualitatively evaluate the dependence of the thermal effect on temperature.
The influence of temperature on the thermal effect is determined by the sign of the value ΔС p (or ΔС V)
At ∆С p > 0 value , that is, with increasing temperature thermal effect increases
at ∆С p< 0 that is, as the temperature increases, the thermal effect decreases.
at ∆С p = 0- thermal effect of the reaction does not depend on temperature
That is, as follows from this, ΔС p determines the sign in front of ΔН.
Heat capacity is the ability to absorb some amount of heat during heating or give it away when cooled. The heat capacity of a body is the ratio of an infinitesimal amount of heat that a body receives to the corresponding increase in its temperature indicators. The value is measured in J/K. In practice, a slightly different value is used - specific heat capacity.
Definition
What does specific heat capacity mean? This is a quantity related to a single amount of a substance. Accordingly, the amount of a substance can be measured in cubic meters, kilograms, or even in moles. What does it depend on? In physics, the heat capacity depends directly on which quantitative unit it refers to, which means that they distinguish between molar, mass and volumetric heat capacity. In the construction industry, you will not meet with molar measurements, but with others - all the time.
What affects specific heat capacity?
You know what heat capacity is, but what values \u200b\u200baffect the indicator is not yet clear. The value of specific heat is directly affected by several components: the temperature of the substance, pressure and other thermodynamic characteristics.
As the temperature of the product rises, its specific heat capacity increases, however, certain substances differ in a completely non-linear curve in this dependence. For example, with an increase in temperature indicators from zero to thirty-seven degrees, the specific heat capacity of water begins to decrease, and if the limit is between thirty-seven and one hundred degrees, then the indicator, on the contrary, will increase.
It is worth noting that the parameter also depends on how the thermodynamic characteristics of the product (pressure, volume, and so on) are allowed to change. For example, the specific heat at a stable pressure and at a stable volume will be different.
How to calculate the parameter?
Are you interested in what is the heat capacity? The calculation formula is as follows: C \u003d Q / (m ΔT). What are these values? Q is the amount of heat that the product receives when heated (or released by the product during cooling). m is the mass of the product, and ΔT is the difference between the final and initial temperatures of the product. Below is a table of the heat capacity of some materials.
What can be said about the calculation of heat capacity?
Calculating the heat capacity is not an easy task, especially if only thermodynamic methods are used, it is impossible to do it more precisely. Therefore, physicists use the methods of statistical physics or knowledge of the microstructure of products. How to calculate for gas? The heat capacity of a gas is calculated from the calculation of the average energy of thermal motion of individual molecules in a substance. The movements of molecules can be of a translational and rotational type, and inside a molecule there can be a whole atom or vibration of atoms. Classical statistics says that for each degree of freedom of rotational and translational movements, there is a molar value, which is equal to R / 2, and for each vibrational degree of freedom, the value is equal to R. This rule is also called the equipartition law.
In this case, a particle of a monatomic gas differs by only three translational degrees of freedom, and therefore its heat capacity should be equal to 3R/2, which is in excellent agreement with experiment. Each diatomic gas molecule has three translational, two rotational and one vibrational degrees of freedom, which means that the equipartition law will be 7R/2, and experience has shown that the heat capacity of a mole of a diatomic gas at ordinary temperature is 5R/2. Why was there such a discrepancy in theory? Everything is due to the fact that when establishing the heat capacity, it will be necessary to take into account various quantum effects, in other words, to use quantum statistics. As you can see, heat capacity is a rather complicated concept.
Quantum mechanics says that any system of particles that oscillate or rotate, including a gas molecule, can have certain discrete energy values. If the energy of thermal motion in installed system is insufficient to excite oscillations of the required frequency, then these oscillations do not contribute to the heat capacity of the system.
In solids, the thermal motion of atoms is a weak oscillation around certain equilibrium positions, this applies to the nodes of the crystal lattice. An atom has three vibrational degrees of freedom and, according to the law, the molar heat capacity solid body equates to 3nR, where n is the number of atoms present in the molecule. In practice, this value is the limit to which the heat capacity of the body tends at high temperatures. The value is achieved with normal temperature changes in many elements, this applies to metals, as well as simple compounds. The heat capacity of lead and other substances is also determined.
What can be said about low temperatures?
We already know what heat capacity is, but if we talk about low temperatures, then how will the value be calculated then? If we are talking about low temperature indicators, then the heat capacity of a solid body then turns out to be proportional T 3 or the so-called Debye's law of heat capacity. The main criterion for distinguishing high temperatures from low ones is the usual comparison of them with a parameter characteristic of a particular substance - this can be the characteristic or Debye temperature q D . The presented value is set by the vibration spectrum of atoms in the product and depends significantly on the crystal structure.
In metals, conduction electrons make a certain contribution to the heat capacity. This part of the heat capacity is calculated using the Fermi-Dirac statistics, which takes electrons into account. The electronic heat capacity of a metal, which is proportional to the usual heat capacity, is a relatively small value, and it contributes to the heat capacity of the metal only at temperatures close to absolute zero. Then the lattice heat capacity becomes very small and can be neglected.
Mass heat capacity
Mass specific heat capacity is the amount of heat that is required to be brought to a unit mass of a substance in order to heat the product per unit temperature. This value is denoted by the letter C and it is measured in joules divided by a kilogram per kelvin - J / (kg K). This is all that concerns the heat capacity of the mass.
What is volumetric heat capacity?
Volumetric heat capacity is a certain amount of heat that needs to be brought to a unit volume of production in order to heat it per unit temperature. It is measured in joules divided by cubic meter per kelvin or J / (m³ K). In many building reference books, it is the mass specific heat capacity in work that is considered.
Practical application of heat capacity in the construction industry
Many heat-intensive materials are actively used in the construction of heat-resistant walls. This is extremely important for houses that are characterized by periodic heating. For example, oven. Heat-intensive products and walls built from them perfectly accumulate heat, store it during heating periods of time and gradually release heat after the system is turned off, thus allowing you to maintain an acceptable temperature throughout the day.
So, the more heat is stored in the structure, the more comfortable and stable the temperature in the rooms will be.
It should be noted that ordinary brick and concrete used in housing construction have a significantly lower heat capacity than expanded polystyrene. If we take ecowool, then it is three times more heat-consuming than concrete. It should be noted that in the formula for calculating the heat capacity, it is not in vain that there is mass. Due to the large huge mass of concrete or brick, in comparison with ecowool, it allows accumulating huge amounts of heat in the stone walls of structures and smoothing out all daily temperature fluctuations. Only a small mass of insulation in all frame houses, despite its good heat capacity, is the weakest area of all frame technologies. To solve this problem, impressive heat accumulators are installed in all houses. What it is? These are structural parts that are characterized by a large mass with a fairly good heat capacity index.
Examples of heat accumulators in life
What could it be? For example, some internal brick walls, a large stove or fireplace, concrete screeds.
Furniture in any house or apartment is an excellent heat accumulator, because plywood, chipboard and wood can actually store heat only per kilogram of weight three times more than the notorious brick.
Are there any drawbacks to thermal storage? Of course, the main disadvantage of this approach is that the heat accumulator needs to be designed at the stage of creating a layout. frame house. This is due to the fact that it is very heavy, and this will need to be taken into account when creating the foundation, and then imagine how this object will be integrated into the interior. It is worth saying that it is necessary to take into account not only the mass, it will be necessary to evaluate both characteristics in the work: mass and heat capacity. For example, if you use gold with an incredible weight of twenty tons per cubic meter as a heat storage, then the product will function as it should only twenty-three percent better than a concrete cube, which weighs two and a half tons.
Which substance is most suitable for a heat storage?
The best product for a heat accumulator is not concrete and brick at all! Copper, bronze and iron do a good job of this, but they are very heavy. Oddly enough, but the best heat accumulator is water! The liquid has an impressive heat capacity, the largest among the substances available to us. Only helium gases (5190 J / (kg K) and hydrogen (14300 J / (kg K)) have more heat capacity, but they are problematic to apply in practice. If you wish and need, see the heat capacity table of the substances you need.
HEAT CAPACITY, the amount of heat expended to change the temperature by 1 ° C. According to a more rigorous definition, heat capacity-thermodynamic. the value determined by the expression:
Where D Q - the amount of heat communicated to the system and caused a change in its t-ry by D T. The ratio of finite differences D Q / D T called. average heat capacity, the ratio of infinitesimal values d Q/dT-true heat capacity. Since d Q is not a total differential of the state function, the heat capacity also depends on the transition path between the two states of the system. There are heat capacity of the system as a whole (J / K), specific heat capacity [J / (g K)], molar heat capacity [J / (mol K)]. In all the formulas below, molar heat capacities are used.
Methods for determining the heat capacity of individual substances. Main experimental the method is calorimetry. Theoretical the calculation of the heat capacity in-in is carried out by the methods of statistical thermodynamics, but it is possible only for relatively simple molecules in the state of an ideal gas and for crystals, and in both cases, an experiment is required for the calculation. data on the structure of the Islands.
Empirical methods for determining the heat capacity in the state of an ideal gas are based on the idea of the additivity of the contributions of individual groups of atoms or chemical. connections. Extensive tables of group atomic contributions to the C p value have been published. For liquids, in addition to additive group methods, methods are used based on the corresponding states of the law, as well as on the use of thermodynamic. cycles that allow passing to the heat capacity of a liquid from the heat capacity of an ideal gas through the temperature derivative of the enthalpy of vaporization.
For p-ra, the calculation of the heat capacity as an additive function of the heat capacity of the components is generally incorrect, because the excess heat capacity of the solution is, as a rule, significant. For its evaluation requires the involvement of molecular-statistical. theories of solutions (see Solutions of non-electrolytes). Experimentally, the excess heat capacity can be determined from temperature dependence enthalpy of mixing, after which it is possible to calculate С р р-ra.
T specific heat capacity of heterog. systems represents naib. difficult case for thermodynamic. analysis. On the state diagram, movement along the phase equilibrium curve is accompanied by a change in both p and T. If the phase equilibrium point shifts during heating, then this gives an addition. contribution to the heat capacity, so the heat capacity of the heterog. system is not equal to the sum of the heat capacities of its constituent phases, but exceeds it. On the phase diagram in the transition from homog. state to the domain of existence of heterog. the heat capacity of the system experiences a jump (see Phase transitions).
Practical value studies of heat capacity is important for energy calculations. process balances in chem. reactors and other chemical apparatuses. pro-va, as well as to select the optimum. coolants. Experiment. measurement of heat capacity for different intervals of tp-from extremely low to high-is the main. method for determining thermodynamic. st-in-in. To calculate the enthalpies and entropies of the island (in the range from 0 to T), integrals of the heat capacity are used.:
corresponding effects are added to the Crimea
The perfection of thermal processes occurring in the cylinder of a real automobile engine is evaluated by the indicator indicators of its actual cycle, while the perfection of the engine as a whole, taking into account power losses due to friction and the drive of auxiliary mechanisms, is evaluated by its effective indicators.
The work done by gases in the cylinders of an engine is called indicator work. The indicator work of gases in one cylinder in one cycle is called cycle work.
It can be determined using an indicator diagram built according to the data of the thermal calculation of the engine.
Area bounded by contour a -c-z"-z-b-a calculated indicator diagram A T , will represent, on an appropriate scale, the theoretical indicator work of gases in one cylinder per cycle. Real diagram area a"-c"-c"-z"-b"-b"-r-a-a" will consist of top and bottom loops. Square A d the upper loop characterizes the positive work of gases per cycle. The boundaries of this loop do not coincide with the calculated ones due to the ignition advance or fuel injection (s "-s- s"-s"), non-instantaneous combustion of fuel (with "-z" -z"-c" and z"- z-z""-z") and prerelease (b"-b-b"-b").
The reduction in the area of the calculation diagram for the indicated reasons is taken into account using diagram completeness factor :
For automotive engines the values of the completeness factor of the diagram take the values 0,93...0,97.
Square An the lower loop characterizes the negative work expended on the pump strokes of the piston for gas exchange in the cylinder. Thus, the actual indicator work of gases in one cylinder in one cycle:
In practice, the value of engine performance per cycle is determined by the average indicated pressure Pi, equal to the useful work of the cycle, referred to the unit of the working volume of the cylinder
Where Wi- useful work of the cycle, J (N m); Vh– working volume of the cylinder, m3.
Average indicator pressure - this is a conditionally constant pressure on the piston during one stroke of the piston, which does work equal to the indicator work of gases for the entire cycle. This pressure is expressed on a certain scale by the height pi rectangle with area A = Hell - An and with a base equal to the length of the indicator chart. Value pi under normal engine operation, it reaches 1.2 MPa in gasoline engines, and 1.0 MPa in diesel engines.
useful work, performed by gases in the engine cylinders per unit time, is called the indicator power and is denoted Pi
.
The indicator work of gases in one cylinder for one cycle is (Nm)
Distinguish between average and true heat capacity. The average heat capacity cn is the amount of heat that is consumed when a unit of gas (1 kg, 1 m3, 1 mol) is heated by 1 K from t1 to t2:
с=q/(t2-t1)
The smaller the temperature difference t2 - t1, the more the value of the average heat capacity approaches the true c. Therefore, the true heat capacity will take place when the value of t2 - t1 approaches zero.
Heat capacity is a function of state parameters - pressure and temperature, therefore, in technical thermodynamics, true and average heat capacities are distinguished.
The heat capacity of an ideal gas depends only on temperature and, by definition, can only be found in the temperature range. However, it can always be assumed that this interval is very small near some temperature value. Then we can say that the heat capacity is determined at a given temperature. This heat capacity is called true.
In the reference literature, the dependence of the true heat capacities with p And with v temperature is given in the form of tables and analytical dependencies. An analytical dependence (for example, for mass heat capacity) is usually represented as a polynomial:
Then the amount of heat supplied in the process in the temperature range [ t1,t2] is determined by the integral:
In the study of thermodynamic processes, the average value of the heat capacity in the temperature range is often determined. It is the ratio of the amount of heat supplied in the process Q 12 to the final temperature difference:
Then, if the dependence of the true heat capacity on temperature is given, in accordance with (2):
Often in the reference literature, values of the average heat capacities are given with p And with v for the temperature range from 0 before t about C. Like true ones, they are presented in the form of tables and functions:
When substituting the temperature value t this formula will be used to find the average heat capacity in the temperature range [ 0.t]. To find the average heat capacity in an arbitrary interval [ t1,t2], using dependence (4), it is necessary to find the amount of heat Q 12 applied to the system in this temperature range. Based on the rule known from mathematics, the integral in equation (2) can be divided into the following integrals:
After that, the desired value of the average heat capacity is found by formula (3).
