Processes isochoric

Isothermal process A constant temperature process Isobaric process A constant pressure process Isochoric process A constant volume process... 

C) CONSTANT-TEMPERATURE CONSTANT-VOLUME (ISOTHERMAL-ISOCHORIC) PROCESSES... 

A constant-volume process is called isochoric and, for such processes, the entropy increase is written as... 

If we draw the two isochores imiii, i 2< 2, on the indicator diagram (Fig. 14), all the paths of change must lie within these limits, which fix the range or amplitude of the process. Let the initial state ( i, T) be a, and let the gas expand isothermally and reversibly to a the maximum work AT is represented by the area aa vtf i, which is shown later to be ... 

The Isochoric Process Figure 2.4 shows the relationship between pcxt and V for an isochoric (constant volume) process going from state a to state b. In this process d V = 0 and tv = 0/... 

In an isothermal process, heat must be added during an expansion and removed during a compression to keep the temperature constant. We will describe this more fully as we now calculate the heat added or removed in isobaric, isochoric, and isothermal processes. 

Equation (2.18) is another example of a line integral, demonstrating that 6q is not an exact differential. To calculate q, one must know the heat capacity as a function of temperature. If one graphs C against T as shown in Figure 2.8, the area under the curve is q. The dependence of C upon T is determined by the path followed. The calculation of q thus requires that we specify the path. Heat is often calculated for an isobaric or an isochoric process in which the heat capacity is represented as Cp or Cy, respectively. If molar quantities are involved, the heat capacities are C/)m or CY.m. Isobaric heat capacities are more... 

We have seen how to calculate q for the isochoric and isobaric processes. We indicated in Chapter 1 that q = 0 for an adiabatic process (by definition). For an isothermal process, the calculation of q requires the application of other thermodynamic equations. For example, q can be obtained from equation (2.3) if AC and w can be calculated. The result is... 

This equation is sometimes called the van t Hoff isochore, to distinguish it from van t Hoff s osmotic pressure equation (Section 8.17). An isochore is the plot of an equation for a constant-volume process. 

Assume isentropic for compression process 1-2, isentropic for compression process 2-3, isochoric for heating process 3-4, isentropic for expansion process 4-5, and isochoric for cooling process 5-6. 

To solve this problem, we build the cycle as shown in Fig. 3.14. Then, (1) assume isobaric for the precooling process 7-8, isentropic for the compression process 8-9, isentropic for the compression process 9-10, isobaric for the heating process 10-11, isentropic for the expansion process 11-12, and isochoric for the cooling process 12-13 (2) input pq= 14.7 psia. 

A cycle called the Atkinson cycle is similar to the Otto cycle except that the isochoric exhaust and intake process at the end of the Otto cycle power stroke is replaced by an isobaric process. The schematic diagram of the cycle is shown in Fig. 3.18. The cycle consists of the following four processes ... 

The isochoric heating process of a Lenoir engine receives air at 15°C and 101 kPa. The air is heated to 2000° C, and the mass of air contained in the cylinder is 0.01kg. Determine the pressure at the end of the isochoric heating process, the temperature at the end of the isentropic expansion process, heat added, heat removed, work added, work... 

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