Gases molar heat capacity

Gases Molar Heat Capacities (cal deg moT ) Liquids Molar Heat Capacities (cal deg" mol ) Solids Specific Heat Capacities (cal deg g )... 

Thermodynamic functions for the ideal gas (molar heat capacity C°, entropy S°, Gibbs free energy function (G°- H298)/T, all in cal- mol K" enthalpy H - HIge in kcal/mol) were calculated from the molecular constants between T = 0 and 6000 K at 100 K intervals [3]. Some values are given on the following page. 

The molar Helmholtz energy A = Af /n of a pure perfect gas may be obtained by integration of eq 3.15 subject to the equation of state, p = —(5 P /5Fm) = nKT/ V, and an expression for the perfect-gas molar heat capacity at constant volume, C y T) = T dS /dT)y. Starting from a reference state defined by temperature T and amount-of-substance density pjf", the result is ... 

The ideal-gas-state heat capacity Cf is a function of T but not of T. For a mixture, the heat capacity is simply the molar average X, Xi Cf. Empirical equations giving the temperature dependence of Cf are available for many pure gases, often taking the form... 

Appendix The Molar Heat Capacities of Gases in the Ideal Gas (Zero Pressure) State... 

Thus, for the ideal gas the molar heat capacity at constant pressure is greater than the molar heat capacity at constant volume by the gas constant R. In Chapter 3 we will derive a more general relationship between Cp m and CV m that applies to all gases, liquids, and solids. 

We have shown that the two molar heat capacities of an ideal gas are related by... 

The molar heat capacity of an ideal gas at constant pressure is greater than that at constant volume the two quantities are related by Eq. 13. 

We can see how the values of heat capacities depend on molecular properties by using the relations in Section 6.7. We start with a simple system, a monatomic ideal gas such as argon. We saw in Section 6.7 that the molar internal energy of a monatomic ideal gas at a temperature T is RT and that the change in molar internal energy when the temperature is changed by AT is A(Jm = jRAT. It follows from Eq. 12a that the molar heat capacity at constant volume is... 

Estimate the molar heat capacity (at constant volume) of sulfur dioxide gas. In addition to translational and rotational motion, there is vibrational motion. Each vibrational degree of freedom contributes R to the molar heat capacity. The temperature needed for the vibrational modes to be accessible can be approximated by 6 = />vvih/, where k is Boltzmann s constant. The vibrational modes have frequencies 3.5 X... 

Hydrochloric acid oxidizes zinc metal in a reaction that produces hydrogen gas and chloride ions. A piece of zinc metal of mass 8.5 g is dropped into an apparatus containing 800.0 mL of 0.500 M HCl(aq). If the initial temperature of the hydrochloric acid solution is 25°C, what is the final temperature of this solution Assume that the density and molar heat capacity of the hydrochloric acid solution are the same as those of water and that all the heat is used to raise the temperature of the solution. 

A sample of nitrogen gas of volume 20.0 L at 5.00 kPa is heated from 20.°C to 400.°C at constant volume. What is the change in the entropy of the nitrogen The molar heat capacity of nitrogen at constant volume, CVm, is 20.81 J-K -mol . Assume ideal behavior. 

C06-0138. According to Table 6H, molar heat capacities of monatomic gases (He, Ar) are significantly smaller than those of diatomic gases (N2, O2, H2). Explain in molecular terms why more heat must be supplied to raise the temperature of I mol of diatomic gas by I K than to raise the temperature of I mol of monatomic gas by 1 K. 

In case a non-linear triatomic gas obeys the principle of equilibration of energies, the molar heat capacity, calculated ... 

Equation (4.36) provides a simple method for estimating an important heat transfer dimensionless group called the Prandtl number. Recall from general chemistry and thermodynamics that there are two types of molar heat capacities, C , and the constant pressure heat capacity, Cp. For an ideal gas, C = 3Cpl5. The Prandtl number is... 

Another observable property of gases is the heat capacity. The molar heat capacity of monatomic gases was measured and found to be equal to (3/2)R, the value predicted for a perfect (point particle) gas. But, actual atoms had a well defined physical size. Since finite spheres would be expected to rotate, where was the heat capacity due to rotation Maxwell worried about this failure of the kinetic theory. Another type of eyes was required to see this result in its proper context. 

The temperature of explosion Te is the maximum temperature that the explosion products can attain under adiabatic conditions. It is assumed that the explosive at an initial temperature Tt is converted to gaseous products which are also at the initial temperature T,. The temperature of these gaseous products is then raised to Te by the heat of explosion Q. Therefore the value of Te will depend on the value of Q and on the separate molar heat capacities of the gaseous products as shown in Equation 5.14, where Cv is the molar heat capacities of the products at constant volume and E represents the summation of the heat capacity integrals corresponding to the separate components of the gas mixture ... 

TABLE 11.2 Measured Thermodynamic Properties (in SI Units) of Some Common Fluids at 20° C, 1 atm Molar Heat Capacity CP, Isothermal Compressibility jS7, Coefficient of Thermal Expansion otp, and Molar Volume V, with Monatomic Ideal Gas Values (cf. Sidebar 11.3) Shown for Comparison... 

Molar heatt capacities at const vol (Cv), of individual products of expln are assumed to be equal to a+b.t, where a is the molar heat capacity at 0°C, b- the increment of the mean molar heat capacity of gas for each 1°C and t - calcd temp of expln... 

It follows that the difference in the molar heat capacities of a ideal gas is... 

Rotation requires energy and leads to higher heat capacities for complex molecules the equipartition theorem can be used to estimate the molar heat capacities of gas-phase molecules, Eq. 22. 

Which gas do you expect to have the higher molar heat capacity, NO or N02 Why ... 

The molar heat capacity of a gas is of the order of 20-32 J K-1 for many gases and AH/T is approximately 84 J K-1 for many normal liquids. Thus, Csat is approximately —50 to — 63 J K 1 that is, approximately 50-63 J of heat must be removed from 1 mole of gas, which is saturated with respect to a liquid or solid, in order to increase its temperature by 1 K. The negative values arise because the molar volume of the saturated gas decreases with increasing temperature. 

However, AH, the difference between the molar enthalpy of the gas and the condensed phase, depends in general on both the temperature and the pressure. The enthalpy for an ideal gas is independent of pressure and, fortunately, the enthalpy for the condensed phase is only a slowly varying function of the pressure. It is therefore possible to assume that AH is independent of the pressure and a function of the temperature alone, provided that the limits of integration do not cover too large an interval. With this final assumption, the integration can be carried out. When the molar heat capacities of the two phases are known as functions of the temperature, AR is obtained by integration. If ACP, the difference in the molar heat capacities of the two phases, is expressed as... 

Thus, the value of (SJ (g) — Sj(/)) at a given temperature may be determined from the slope of the curve of In xt plotted as a function of In T at the given temperature, provided that (d Afi2/dx2)T P can be evaluated from experiment or theory. Similarly, (H (g) — f j(/)) can be calculated at a given temperature from the slope of the curve of In xt plotted as a function of 1/T at the given temperature with the same provision. The values so determined are not isothermal when isothermal values are desired, then a knowledge of the partial molar heat capacity of the solvent in the liquid phase and the molar heat capacity of the component in the gas phase would be required. 

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