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Imagine that your dog has eaten the portion of Table 4.1 that gives entropy data; only the enthalpy data remains. Explain how you could reconstruct the missing portion of the table. Use your method to explicitly check a few of the entries for consistency. How much of Table 4.2 could you reconstruct if it were missing? Explain.

Short Answer

Expert verified

We can say that the missing portion of table 4.1 is reconstructed by applying the second law of thermodynamics and the table 4.2.


Step by step solution

01

Given information

Given table 4.1

And Table 4.2

02

Explanation

First express the change in entropy for steam at zero temperature
ΔS1=QT......(1)
Where, Q is the heat change (absorbed or lost) and T is the temperature.

We know that the enthalpy is described as the energy that is required to produce a substance at fixed pressure.

Now write an expression of the change in entropy for water at given temperature
ΔS2=ΔHT......(2)
Where, ΔH- change in enthalpy

Substitute Q = 2501 kJ/kg and T =273 K in equation (1), we get
ΔS1=2501kJ·kg-1(273K)=9.156kJ·kg-1·K-1
This is the same value as in Table

Now, substitute ΔH=42kJ·kg-1and T=278 K in equation (2), we get

ΔS2=42kJ.kg-1(278K)=0.151kJ·kg-1.K-1

This value is the same as in given table

Now write expression for the change in entropy for steam at given temperature
ΔS=ΔHT-nRΔPP......(3)
Where, n is number of moles, R is gas constant, P is average pressure and ΔPis change in pressure.

Substitute ΔH=19kJ·kg-1, T=278K, n= 55.55, R= 8.314 J/mole K,ΔP= 0.006 and P=0.009 bar in expression (3), we get

ΔS=19kJ·kg-1(278K)-(55.55)(8.314J/mole·K)(0.006bar)(0.009bar)=-0.239kJ·kg-1·K-1

The entropy for steam at finite temperature is:

ΔS1+ΔS=9.156kJ·kg-1·K-1+-0.239kJ·kg-1·K-1=8.917kJ·kg-1·K-1

This value is very close to the value in the table.

So we can say that the missing portion of table 4.1 is reconstructed by applying the second law of thermodynamics and the table 4.2.


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Most popular questions from this chapter

Imagine that your dog has eaten the portion of Table 4.1 that gives entropy data; only the enthalpy data remains. Explain how you could reconstruct the missing portion of the table. Use your method to explicitly check a few of the entries for consistency. How much of Table 4.2 could you reconstruct if it were missing? Explain.

Liquid HFC-134a at its boiling point at 12 bars pressure is throttled to 1 bar pressure. What is the final temperature? What fraction of the liquid vaporizes?

Table 4.3. Properties of the refrigerant HFC-134a under saturated conditions (at its boiling point for each pressure). All values are for 1kgof fluid, and are measured relative to an arbitrarily chosen reference state, the saturated liquid at -40°c. Excerpted from Moran and Shapiro (1995).

The amount of work done by each stroke of an automobile engine is controlled by the amount of fuel injected into the cylinder: the more fuel, the higher the temperature and pressure at points 3 and 4 in the cycle. But according to equation 4.10, the efficiency of the cycle depends only on the compression ratio (which is always the same for any particular engine), not on the amount of fuel consumed. Do you think this conclusion still holds when various other effects such as friction are taken into account? Would you expect a real engine to be most efficient when operating at high power or at low power? Explain.

Consider an ideal Hampson-Linde cycle in which no heat is lost to the environment.

(a) Argue that the combination of the throttling valve and the heat exchanger is a constant-enthalpy device, so that the total enthalpy of the fluid coming out of this combination is the same as the enthalpy of the fluid going in.

(b) Let xbe the fraction of the fluid that liquefies on each pass through the cycle. Show that

x=Hout-HinHout-Hliq,

where Hinis the enthalpy of each mole of compressed gas that goes into the heat exchanger, Houtis the enthalpy of each mole of low-pressure gas that comes out of the heat exchanger, and Hliqis the enthalpy of each mole of liquid produced.

(c) Use the data in Table 4.5to calculate the fraction of nitrogen liquefied on each pass through a Hampson-Linde cycle operating between 1 bar and 100 bars, with an input temperature of 300K. Assume that the heat exchanger works perfectly, so the temperature of the low-pressure gas coming out of it is the same as the temperature of the high-pressure gas going in. Repeat the calculation for an input temperature of 200K.

At a power plant that produces 1 GW109 watts) of electricity, the steam turbines take in steam at a temperature of 500o, and the waste heat is expelled into the environment at 20o
(a) What is the maximum possible efficiency of this plant?
(b) Suppose you develop a new material for making pipes and turbines, which allows the maximum steam temperature to be raised to 600o. Roughly how much money can you make in a year by installing your improved hardware, if you sell the additional electricity for 5 cents per kilowatt-hour? (Assume that the amount of fuel consumed at the plant is unchanged.)

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