Max Work from 800 ıC Brick Cooling to 25 ıC

[seeveedubyah]

Homework Statement

A young engineer notices in her plant that 1-kg blocks of brick are routinely removed from a 800 ıC oven and are let to cool in air at 25 ıC. Conscious about cost-cutting and efficiency, she wonders whether some work could be recovered from this process. Calculate the maximum amount of work that could be obtained. The CP of brick is 0.9 kJ/kg K. Can you come up with devices that could extract this work?

Homework Equations

Q=ΔH, ΔU=W+Q, η=1-Tl/Th,

The Attempt at a Solution

I know that a reversible process is the best option do so. This is most likely going to be done with a carnot cycle to extract the work. I'm not sure if the T of the air given is going to be any help. The bricks being 1kg can be relevant to how much thermal energy it has. Don't do this with Q=mCpΔT because we used in basic chemistry thermo so he doesn't want us to use that in this class.

 

[RTW69]

It isn't clear to me why W=m*C_p*ΔT isn't appropriate. Assuming the air is a large heat sink of constant temperature the brick will cool to air temperature. That equation should be appropriate.

 

[seeveedubyah]

That equation would work for the brick but not air or water since Cp is actually calculated from tabulated values which depend on temperature and pressure.

 

[rude man]

Homework Statement

A young engineer notices in her plant that 1-kg blocks of brick are routinely removed from a 800 ıC oven and are let to cool in air at 25 ıC. Conscious about cost-cutting and efficiency, she wonders whether some work could be recovered from this process. Calculate the maximum amount of work that could be obtained. The CP of brick is 0.9 kJ/kg K. Can you come up with devices that could extract this work?

Homework Equations

Q=ΔH, ΔU=W+Q, η=1-Tl/Th,

The Attempt at a Solution

I know that a reversible process is the best option do so. This is most likely going to be done with a carnot cycle to extract the work. I'm not sure if the T of the air given is going to be any help. The bricks being 1kg can be relevant to how much thermal energy it has. Don't do this with Q=mCpΔT because we used in basic chemistry thermo so he doesn't want us to use that in this class.

Carnot is out since that cycle operates between two constant temperatures. Your T2 is constant at 25C but your T1 is not.

Reversible cycle, yes. Be guided by the 1st and 2nd laws. While the entropy increase S2 of the cooling medium is just Q2/T, T = 25 + 273, S1 will be an integral over the temp. drop of the brick and will of course be negative.

So Q1 = Q2 + W but S2 + S1 > 0.

 

[rezeew]

I would approach this problem by first calculating the heat energy lost by the bricks as they cool from 800 ıC to 25 ıC. This can be done using the formula Q=mCpΔT, where m is the mass of the bricks, Cp is the specific heat capacity of the bricks, and ΔT is the change in temperature.

Once the heat energy lost is calculated, I would then use the formula ΔU=W+Q to determine the maximum amount of work that could be obtained from this process. This formula takes into account the change in internal energy and the heat energy lost, and the resulting value would represent the maximum amount of work that could be extracted from the cooling bricks.

In terms of devices that could extract this work, a possible option could be a heat engine that operates on a Carnot cycle. This cycle would use the temperature difference between the hot bricks (800 ıC) and the cool air (25 ıC) to convert thermal energy into mechanical work. Other possible devices could include thermoelectric generators or Stirling engines.

Overall, it is important to note that the efficiency of any device extracting work from this process would be limited by the Carnot efficiency η=1-Tl/Th, where Tl is the temperature of the cool air and Th is the temperature of the hot bricks. Therefore, in order to extract the maximum amount of work, it would be necessary to have a large temperature difference between the hot and cool sources.