Multiple temperature reservoirs

[cabellos]

I have a problem:

A typical compartment domestic refrigerator with freezer can be represented by 3 temperature reservoirs connected to the cyclic device which absorbs W' of work.

- cool box at Tc = +279K from which Q'c heat is extracted
- freezer at Tf = -269k from which a further Q'f heat is extracted
-Domestic ambient surroundings at T = 298K to which Q'rej heat is rejected

Assuming ideal reversible performance calculate the maximum physically possible rate of heat extraction Q'f (W) from the freezer compartment for Q'c = 100W

How do you calculate this WITHOUT knowing Q'rej is the first place?

confused

thankyou for your time,

Cabellos

 

[Valkarie]

Without knowing the value of Q'rej, it is not possible to calculate the maximum physically possible rate of heat extraction Q'f from the freezer compartment. However, you can use the conservation of energy law to determine an expression for Q'f in terms of Q'c and Q'rej. This equation is given by: Q'f = Q'c + Q'rej. Therefore, if you know the values of Q'c and Q'rej, you can then solve for Q'f.

 

[piercas]

I understand your confusion and I am happy to explain the calculation process to you. In order to calculate the maximum possible rate of heat extraction from the freezer compartment, we need to use the concept of the second law of thermodynamics.

The second law of thermodynamics states that heat always flows from a higher temperature reservoir to a lower temperature reservoir. This means that in a refrigeration system, heat will flow from the cool box at Tc to the freezer at Tf, and then to the ambient surroundings at T.

Now, in order to calculate the maximum possible rate of heat extraction, we need to consider the efficiency of the refrigeration cycle. The efficiency of a refrigeration cycle is defined as the ratio of the heat extracted from the cool box (Q'c) to the work input (W'). Mathematically, it can be written as:

Efficiency = Q'c / W'

Since we know Q'c = 100W, we can rearrange the equation to solve for W':

W' = Q'c / Efficiency

Now, we need to determine the efficiency of the refrigeration cycle. This can be done by using the Carnot efficiency formula, which is given by:

Efficiency = (Tc - Tf) / Tc

Where Tc is the temperature of the cool box and Tf is the temperature of the freezer.

Plugging in the values for Tc and Tf, we get:

Efficiency = (279K - (-269K)) / 279K = 1.964

Now, we can substitute this value of efficiency in the equation we derived earlier to calculate the maximum possible rate of heat extraction from the freezer compartment:

W' = 100W / 1.964 = 50.97W

Therefore, the maximum possible rate of heat extraction from the freezer compartment is 50.97W. This calculation does not require knowledge of Q'rej as it is based on the fundamental principles of thermodynamics. I hope this explanation helps to clear up your confusion. Let me know if you have any further questions.