Exergy value at double temperature

[gfd43tg]

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 Tσ 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?

 

[rude man]

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?

 

[gfd43tg]

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?

 

[rude man]

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.

 

[rezeew]

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.