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Does the relation Cp minus Cv equal R hold true for solids and liquids Why or why not?
No, this relation is ONLY for ideal gases. The difference between Cp and Cv can be written more generally as T*(dP/dT)v*(dV/dT)p, where the lower case v and p represent the derivatives taken at constant volume and pressure, respectively. If you take these two derivatives using the ideal gas law (PV=nRT), then the result simplifies to Cp-Cv=R. However, solids and liquids do not follow the ideal gas law, and the difference between Cp and Cv is much smaller... negligible in many cases. For solids, Cp-Cv can be calculated using the isobaric expansivity, isothermal compressibility, and density of the material.
What are the differences between the specific heat capacities (cp) and molar heat capacities (cv) of a substance, and how do they relate to the number of degrees of freedom (nr) in the system?
The specific heat capacity (cp) of a substance measures the amount of heat needed to raise the temperature of a unit mass of the substance by 1 degree Celsius, while the molar heat capacity (cv) measures the heat needed to raise the temperature of one mole of the substance by 1 degree Celsius. The relationship between cp and cv is given by the equation cp cv R, where R is the gas constant. The number of degrees of freedom (nr) in a system is related to the molar heat capacity through the equation cv (nr/2)R. This means that the molar heat capacity is directly proportional to the number of degrees of freedom in the system.
What is a monatomic compound?
In physics and chemistry, monatomic is a combination of the words "mono" and "atomic," and means "single atom." It is usually applied to gases: a monatomic gas is one in which atoms are not bound to each other. At standard temperature and pressure (STP), all of the noble gases are monatomic. These are helium, neon, argon, krypton, xenon and radon. The heavier noble gases can form compounds, but the lighter ones are unreactive. All elements will be monatomic in the gas phase at sufficiently high temperatures. The only mode of motion of a monatomic gas is translation (electronic excitation is not important at room temperature). Thus in an adiabatic process, monatomic gases have an idealised γ-factor (Cp/Cv) of 5/3, as opposed to 7/5 for ideal diatomic gases where rotation (but not vibration at room temperature) also contributes. Also, for ideal monatomic gases: : the molar heat capacity at constant pressure (Cp) is 2.5 R = 20.8 J K-1 mol-1 (4.97 cal K-1 mol-1); : the molar heat capacity at constant volume (Cv) is 1.5 R= 12.5 J K-1 mol-1 (2.98 cal K-1 mol-1); where R is the gas constant.
What is Specific heat at constant volume of natural gas?
Assuming your natural gas is 100% methane, the specific heat at constant pressure at 25°C:Cp/R = 4.217where R is the ideal gas constant represented in terms of energy.Using R=8.314 Joule/(Kelvin*mole)This yields Cp=35.06 J/(K*mol)The heat capacity at constant volume, Cv, is related to the heat capacity at constant pressure, Cp by the following expression:Cp-Cv=RTherefore Cv=Cp-R = 35.06 J/(K*mol) - 8.314 J/(K*mol) = 26.75 J/(K*mol)Assumptions:The system is a monotonic ideal gasThe temperature is at or near 25°CHeat capacity is not a function of temperatureA more accurate heat capacity as a function of temperature isCp/R = 1.702 + 9.081E-3*T - 2.164*T^(-2)where T is in Kelvins from 298K (25°C) to 1500K (1226.85°C)Assumptions 2 and 3 above do not apply to this.Source: Introduction to Chemical Engineering Thermodynamics. 7th Ed. by J.M. Smith, Appendix C p. 684
Why does a diatomic gas have greater energy content per mole than monoatomic gas at the same temperature?
The molar specific heat of a diatomic molecule is CV = (5/2) R, meaning U = (5/2) n R T, while, for a monatomic gas, CV = (3/2) R or U = (3/2) n R T. Since the molar specific heat is greater for a diatomic molecule, there is more internal energy stored inthe motion of the molecules for the same temperature than for that temperature in a monatomic gas.
What is the significance of the cp/cv ratio in thermodynamics and how does it affect the behavior of gases?
The cp/cv ratio in thermodynamics is important because it helps determine how gases behave when heated or cooled. Specifically, it affects how much a gas's temperature changes when it absorbs or releases heat. Gases with a higher cp/cv ratio tend to experience larger temperature changes for the same amount of heat added or removed, while gases with a lower ratio have smaller temperature changes. This ratio is crucial in understanding and predicting the behavior of gases in various thermodynamic processes.
Does the relation Cp minus Cv equal R hold true for solids and liquids Why or why not?
No, this relation is ONLY for ideal gases. The difference between Cp and Cv can be written more generally as T*(dP/dT)v*(dV/dT)p, where the lower case v and p represent the derivatives taken at constant volume and pressure, respectively. If you take these two derivatives using the ideal gas law (PV=nRT), then the result simplifies to Cp-Cv=R. However, solids and liquids do not follow the ideal gas law, and the difference between Cp and Cv is much smaller... negligible in many cases. For solids, Cp-Cv can be calculated using the isobaric expansivity, isothermal compressibility, and density of the material.
What Cv and Cp of air?
1.005
What has the author Wilbert Frederick Koehler written?
Wilbert Frederick Koehler has written: 'The ratio of the specific heats of gases, Cp/Cv, by a method of self-sustained oscillations' -- subject(s): Heat, Gases
Why cp and cv have different values?
Cv is a for a constant volume, and there is therefore no work done in the expansion whereas as Cp accounts for the work done by the gas during its expansion, as well as the change in its internal energy. Thusly Cp is generally bigger than Cv. Intuitively this would be very simple to work out yourself. We used to have to work this out ourselves back in my day, not just resort to cheap answers on the interweb.
How do you derive the equation cp-cv equals R?
The equation Cp - Cv = R is derived from the first law of thermodynamics applied to an ideal gas process. It relates the specific heat capacities at constant pressure (Cp) and constant volume (Cv) of an ideal gas to the universal gas constant (R). This relationship is based on the assumption that the internal energy of an ideal gas depends only on its temperature.
Why Cp is greater Cv?
Because Cp has two functions:- 1-To change the internal energy dU. 2-To do work dW in expanding the gas. Where as Cv has only one function of changing the internal energy of the gas..by awais
Is CV an energy unit?
CV can refer to two different energy units: In the context of heat energy, CV stands for Calorific Value, which is the amount of heat produced by a unit mass of a fuel when it is burned completely. In the context of electricity, CV stands for Capacity Value, which represents the contribution of a power plant or energy source to the overall capacity of the grid.
Why Cp is greater than Cv?
Because Cp has two functions:- 1-To change the internal energy dU. 2-To do work dW in expanding the gas. Where as Cv has only one function of changing the internal energy of the gas....by Hamoud Seif
Give expression for efficiency of dual cycle?
= 1 - qout/qin = 1 - cv(T4-T1)/(cv(Tx-T2)+cp(T3-Tx))
Do gases have specific heats?
Yes. Two specific heats are commonly defined: CV (constant volume specific heat and CP (constant pressure specific heat). For an ideal gas the relationship between the two can be calculated to be CP = CV + R The theoretical value of the specific heats for ideal gases can be estimated from the degrees of freedom of the gas - which in turn depends on it's structure. Monatomic gases really can only absorb energy by increasing their translational energy or boosting the electrons to higher orbitals. Diatomic gases add a degree of freedom for vibration and another for rotation (although diatomic molecules usually can store only and insignificant amount of energy in their rotations. Polyatomic molecules with more than two atoms have even greater degrees of freedom because they pick up vibrational modes for the additional molecular bonds and more rotational modes.
Explain how you can determine the atomicity of a gas?
To find the atomicity of an ideal gas you can use γ = Cp/Cv.
