Saturated water vapor at 400^∘ F is expanded while its pressure is kept constant until its tempe

Saturated water vapor at 400^∘ F is expanded while its...

Key Concepts

Departure Charts

Departure charts are graphical tools used to adjust or correct the idealized thermodynamic properties (often assumed under ideal gas conditions) to account for the real behavior of substances. They are particularly useful when dealing with fluids like water that deviate from ideal behavior at certain temperatures and pressures, allowing more accurate estimates of properties such as enthalpy and entropy.

Specific Entropy

Specific entropy quantifies the degree of disorder or randomness per unit mass in a system. It is a fundamental concept in thermodynamics that helps in assessing the irreversibility of a process and in determining the feasibility of a reaction or phase change. Changes in specific entropy are central to the second law of thermodynamics and are essential in analyzing the efficiency of thermodynamic processes.

Property Tables

Property tables, such as steam tables, provide tabulated values of thermodynamic properties like temperature, pressure, specific enthalpy, and specific entropy for a substance under various states, including saturated and superheated conditions. They are indispensable tools in thermodynamics for directly reading or interpolating the required property values, ensuring precise calculations in engineering analyses.

Isobaric Process

An isobaric process is one that occurs at a constant pressure. In thermodynamics, analyzing such processes involves tracking changes in temperature, volume, and internal energy while the pressure remains fixed. This concept is important when studying the behavior of fluids as they expand or compress, as it directly affects the calculation of state properties such as enthalpy and entropy.

Saturated Vapor

Saturated vapor refers to a state in which a substance, typically a liquid like water, is in equilibrium with its vapor at a given pressure and temperature. In this condition, the liquid and vapor phases coexist, and any added heat can cause phase change without a temperature change. Understanding saturated vapor is crucial for evaluating the properties of a fluid during phase transitions and for determining the boundary between different phases in thermodynamic processes.

Specific Enthalpy

Specific enthalpy is a property that represents the total energy content per unit mass of a substance, including both its internal energy and the energy required to make room for it by displacing its environment (flow work). It is a key thermodynamic parameter in energy balance calculations, especially in processes involving heat transfer, phase changes, or work interactions.

Transcript

00:01 For this problem on the topic of thermodynamic property relations, we are told that saturated water vapor is expanded while its pressure is kept constant to a higher temperature.

00:13 We want to calculate the change in specific enthalpy and entropy using firstly the departure charts as well as the property tables.

00:22 So if we were to use the departure charts, we first made the pressure of water vapor during this process.

00:29 So p1 is equal to p2, the pressure is kept constant, and this is the saturation pressure at our temperature of 400 degrees fahrenheit.

00:44 And from our tables, we know this to be 247 .26 pounds per square inch absolute.

00:57 Now if we go to our ideal gas property table for water vapor, we can find p -chane.

01:03 In enthalpy h bar 2 minus h bar 1 for an ideal water vapor and a motor basis to be 10 ,354 .9 minus 6 ,8955 .6, which gives an enthalpy change during this process of 3 ,459 .3 btu -pan -moe.

01:46 So we have the change in entropy on a molar basis.

01:51 Similarly the change in entropy on a molar basis is s2 bar minus s1 bar again we assume an ideal gas behavior and this is equal to the temperature dependent entropy s2 minus the temperature dependent entropy s1 -0 minus the universal gas constant ru times the natural log of the ratio of pressures p2 over p1.

02:26 And so if we substitute our values into this, this becomes 52 .212 minus 48 .916.

02:37 And obviously the last term becomes zero since p2 and p1 are the same.

02:42 So the natural log of 1 becomes zero.

02:45 This gives us the change in entropy on a molar basis to be 3 .296 btu per pound mole r.

03:03 Now the enthalpy and entropy departures of water vapor at the given states can be determined from the generalized charts.

03:11 And we can do this by first calculating the reduced temperature of the initial state tr1 is the specific temperature t1 over the critical temperature tc.

03:23 And so this is 860 rankin divided by 1 ,164 .8 rankin, which gives us a relative or reduced temperature of 0 .730.

03:41 0.

03:43 The reduced pressure of the first state pr1 is equal to p1 over the critical pressure pc, and that's 247 .26, which we found above, over 3 ,200.

04:02 And simplifying, we get a reduced pressure of 0 .0727.

04:10 So from these values, we find the enthalpy departure, zh1 to be 0 .1342, and our entropy departure of the first state, zs1, to be 0 .1171.

04:32 Now we can do the same for the second state.

04:37 So the reduced temperature of the second state, tr2, is equal to the specific temperature temperature t2 over the critical temperature of water vapor tc and this is 1 ,260 ranken over 1 ,164 .8 which gives us the reduced temperature of 1 .08 of 1 .081 and it reduced pressure pr2 which is p2 over pc and this is 680 80 .56 divided by the critical pressure of 3 ,200.

05:30 So actually no, it's the pressure is constant and so the pressure is 247 .26.

05:43 So the pressure does not change over 3 ,200 which again is 0 .07727.

05:50 So the reduced pressure remains constant as well.

05:56 And this from our generalized charts gives us an entropy departure zh2 of 0 .07213, an entropy departure zs2 of 0 .04595.

06:18 So we can calculate the entropy and entropy changes per most.

06:22 Basis as follows.

06:28 So per mole we get the change in enthalpy h2 bar minus h1 bar to be the change in enthalpy on a molar basis for the ideal gas h2 bar minus h1 bar minus the universal gas constant ru times the critical temperature tc times the change in enthalpy departure is in h2 minus zh1...

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