Heat capacity entropy change

So what macroscopic properties do we mean Well, those that are connected with heat q) and work (w), of course. Water is an important agent in the transport of heat, such as in convecting systems, but this is not really a thermodynamic subject. By connected with heat I mean things like the heat capacity, entropy, and enthalpy of water itself, and how changes in these properties are of interest. The property connected with work is of course the molar or specific volume. 

In many ways the most valuable application of the data of infrared and Raman studies is to the calculation of the heat capacity, entropy, and free energy of gaseous molecules. For such calculations a knowledge of the moments of inertia and vibration frequencies of the molecule is necessary. Calculations of this sort have been carried out for a large number of simple molecules with results which usually surpass in accuracy those of any other method. If the value for the heat of reaction is known at any temperature, spectroscopic data can be used to find the heat of the reaction at any other temperature, the free energy and entropy changes, and the equilibrium constant at any temperature. 

Tables edited by Allard provide information on metals, including phase changes, vapour pressures, heat capacities, entropies, and enthalpies.

A lustrous metal has the heat capacities as a function of temperature shown in Table 1-4 where the integers are temperatures and the floating point numbers (numbers with decimal points) are heat capacities. Print the curve of Cp vs. T and Cp/T vs. T and determine the entropy of the metal at 298 K assuming no phase changes over the interval [0, 298]. Use as many of the methods described above as feasible. If you do not have a plotting program, draw the curves by hand. Scan a table of standard entropy values and decide what the metal might he. 

In this approximation it is assumed drat die endialpy of exchange is equal to the energy of exchange, and the thermal entropy of exchange is equal to zero. Both of diese imply that there is no change in heat capacity when this exchange is carried out, which is not normally the case, although the effect is small. 

If the heat capacity can be evaluated at all temperatures between 0 K and the temperature of interest, an absolute entropy can be calculated. For biological processes, entropy changes are more useful than absolute entropies. The entropy change for a process can be calculated if the enthalpy change and free energy change are known. 

When a substance is heated at constant pressure without change of phase through a temperature rise dr the heat absorbed is Cp dr, where Cp is the molar heat capacity at constant pressure, and the entropy increase is... 

Equation (4.2) can be used to determine the entropy of a substance. A pure crystalline sample is placed in a cryogenic calorimeter and cooled to low temperatures. Increments of heat, q, are added and the temperature change, AT, is measured, from which the heat capacity can be calculated from the relationship... 

We have shown that, provided the heat capacity can be treated as constant in the temperature range of interest, the entropy change that occurs when a system is heated from T, to T2 is given by... 

What does this equation tell us If T2 is higher than T, then T2/T, > 1, the logarithm of this ratio is positive, and therefore AS is positive too, corresponding to the expected increase in entropy as the temperature is raised. The greater the heat capacity of the substance, the greater the increase in entropy for a given change in temperature. 

Figure 7.3 shows how the entropy of a substance changes as it is heated through a temperature range in which it has a constant heat capacity. 

FIGURE 7.3 The change in entropy as a sample is heated for a system with a constant heat capacity (O in the range of interest. Here we have plotted AS/C. The entropy increases logarithmically with temperature. 

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. 

STRATEGY We expect a positive entropy change because the thermal disorder in a system increases as the temperature is raised. We use Eq. 2, with the heat capacity at constant volume, Cv = nCV m. Find the amount (in moles) of gas molecules by using the ideal gas law, PV = nRT, and the initial conditions remember to express temperature in kelvins. Because the data are liters and kilopascals, use R expressed in those units. As always, avoid rounding errors by delaying the numerical calculation to the last possible stage. 

Self-Test 7.2B The temperature of 5.5 g of stainless steel is increased from 20.°C to 100.°C. What is the change in the entropy of the stainless steel The specific heat capacity of stainless steel is 0.51 J-(°C) -g 1. 

The change in entropy on heating is calculated from the heat capacity and the temperature, as we did in Example 7.2. However, because we cannot assume that the heat capacity is constant all the way down to T = 0, we have to use a more general expression. 

Assuming that the heat capacity of an ideal gas is independent of temperature, calculate the entropy change... 

Assuming that the heat capacity of an ideal gas is independent of temperature, calculate the entropy change associated with lowering the temperature of 2.92 mol of ideal gas atoms from 107.35°C to —52.39°C at (a) constant pressure and (b) constant volume. 

Change in entropy when a substance of constant heat capacity, C, is heated from T, to T2 ... 

Quite similar equations can be formulated for AG and AH by use of the partition function f of the activated complex. It follows from equations (6) and (7) that AEp can only be evaluated if the partition functions and AEz are available from spectroscopic data or heat capacity measurements. However, if AG = AH, the entropy change AS equals zero, and if AEz also equal to zero, either AG or AH can then be identified with the potential energy change. If... 

In most processes, a reversible absorption of heat is accompanied by a change in temperature, and a calculation of the corresponding entropy change requires an evaluation of the integral of q/T. The term q is related to the heat capacity of the system which is usually expressed as a function of temperature. In a constant volume process, for example, the entropy change is... 

The limitation of the storage capacity is, as mentioned before, caused by the limitation of entropy change AS within the storage (see Figure 4). For sensible and latent heat storage (so-called direct thermal energy storage) this is defined by the specific heat... 

Ammonium salts such as NH4C1 are sometimes observed to undergo an abrupt change in heat capacity (and hence entropy) at some temperature below the melting point. Describe the processes likely responsible for these observations. 

---