Exergy value at double temperature

In summary: So, is C constant or not? If not, then I guess you would have to do some calculus to get the exact Wlost and Wideal.In summary, the conversation discusses the relationship between heat and exergy at different temperatures. It is revealed that exergy is the maximum useful work that can be achieved and the lost work of a process is determined by the surrounding absolute temperature. It is then suggested that the work lost at zero K would be zero, and that all the heat extracted at a certain temperature can go into work. However, it is also mentioned that the specific heat capacity (C) may vary with temperature, making it necessary to use calculus to calculate the exact values for Wlost and Wideal.
  • #1
gfd43tg
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HS2: Does heat at 400°C carry two times exergy value than heat a 200 °C? If not, how much should it be?

Exergy is the maximum useful work that can be achieved. The lost work of a process is

##W_{lost} = T_{\sigma}\Delta S - Q##

Where is the surrounding absolute temperature.

If the Exergy is ##W_{ideal} - W_{lost}##, then

##Exergy_{400} = W_{ideal} - (673 K)\Delta S + Q##
##Exergy_{200} = W_{ideal} - (473 K)\Delta S + Q##

Subtracting these equations,

##Exergy_{400} - Exergy_{200} = -200 \Delta S##
##Exergy_{400} = -200 \Delta S + Exergy_{200}##

Which is clearly not the same as a doubling in value. Is this the right way to do it?
 
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  • #2
This is just my shot at it, look for others to respond also:

I don't know about your Wlost formula. Never seen it. But if the surroundings are at zero K, is the work lost = -Q? I would think zero instead.

Since the low temperature T2 can be zero K, all the heat extracted at T = T1 can go into work. So W = Q1. But Q1 = C*T1. So assuming C constant between 200C and 400C, what W can be extracted at each temperature?
 
  • #3
So then you would say for 400C, then ##Exergy_{400} = C_{p}(673K)##, and ##Exergy_{200} = C_{p}(473 K)##, which still would not be double?
 
  • #4
Maylis said:
So then you would say for 400C, then ##Exergy_{400} = C_{p}(673K)##, and ##Exergy_{200} = C_{p}(473 K)##, which still would not be double?

Yes, except I'm not sure if it would be ##C_{p}## or ##C_{V}## or something else. I guess it would depend on the system. I would just call it C. In reality C would be a function of temperature anyway, for such a large range of temperatures all the way down to zero K.
 
  • #5


Yes, this is the correct way to calculate the exergy value at different temperatures. It is important to note that the exergy value is not solely dependent on temperature, but also on the entropy change and the heat transfer. Therefore, it is not accurate to say that heat at 400°C carries two times the exergy value than heat at 200°C. The exergy value will depend on the specific process and the surrounding temperature.
 

1) What is the definition of "Exergy value at double temperature"?

The exergy value at double temperature is a measure of the maximum work that can be obtained from a system when it is brought into thermal equilibrium with its surroundings at a higher temperature and then cooled to a lower temperature. It takes into account both the temperature difference and the quality of the energy source.

2) How is the exergy value at double temperature calculated?

The exergy value at double temperature is calculated by multiplying the energy input at the higher temperature by the exergy efficiency, which is the ratio of the actual work output to the maximum possible work output. This calculation takes into account the exergy losses due to irreversibilities within the system.

3) What is the significance of the exergy value at double temperature?

The exergy value at double temperature is a useful tool for evaluating the potential for energy efficiency and the quality of different energy sources. It provides a more comprehensive measure than just energy value, as it takes into account the thermodynamic properties of the system.

4) Can the exergy value at double temperature be negative?

Yes, the exergy value at double temperature can be negative. This occurs when the energy input to the system is of low quality and the exergy efficiency is less than one. In this case, the work output would be less than the maximum possible work, resulting in a negative exergy value.

5) How can the exergy value at double temperature be improved?

The exergy value at double temperature can be improved by increasing the exergy efficiency, either through technological improvements or by using higher quality energy sources. Reducing exergy losses within the system can also help to improve the exergy value at double temperature.

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