An ordinary egg can be approximated as a 5.5-cm- diameter sphere. The egg is initially at a unif

An ordinary egg can be approximated as a 5.5-cm- diameter...

An ordinary egg can be approximated as a $5.5-\mathrm{cm}-$ diameter sphere. The egg is initially at a uniform temperature of $8^{\circ} \mathrm{C}$ and is dropped into boiling water at $97^{\circ} \mathrm{C}$. Taking the properties of egg to be $\rho=1020 \mathrm{kg} / \mathrm{m}^{3}$ and $c_{p}=3.32 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C}$ determine how much heat is transferred to the egg by the time the average temperature of the egg rises to $70^{\circ} \mathrm{C}$ and the amount of exergy destruction associated with this heat transfer process. Take $T_{0}=25^{\circ} \mathrm{C}$.

An ordinary egg can be approximated as a $5.5-\mathrm{cm}-$ diameter sphere. The egg is initially at a uniform temperature of $8^{\circ} \mathrm{C}$ and is dropped into boiling water at $97^{\circ} \mathrm{C}$. Taking the properties of egg to be $\rho=1020 \mathrm{kg} / \mathrm{m}^{3}$ and $c_{p}=3.32 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C}$
determine how much heat is transferred to the egg by the time the average temperature of the egg rises to $70^{\circ} \mathrm{C}$ and the amount of exergy destruction associated with this heat transfer process. Take $T_{0}=25^{\circ} \mathrm{C}$.

Key Concepts

Reference Environment

In exergy analysis, the reference environment is the state (often defined by ambient temperature and pressure) against which the work potential of a system is measured. It represents the baseline condition where energy is considered to have no available work potential, and it is crucial for accurately determining the exergy and exergy destruction associated with any thermal process.

Exergy Destruction

Exergy destruction quantifies the loss of potential work due to irreversibilities during a process, such as heat transfer across finite temperature differences. It represents the portion of input energy that cannot be used to perform work because of inherent inefficiencies, and is typically calculated by considering the difference between the energy transferred and the corresponding exergy value using the appropriate Carnot efficiency factor.

Sensible Heat Transfer

This concept refers to the energy required to raise the temperature of a substance without undergoing a phase change. It is determined by the product of the mass, specific heat capacity, and the change in temperature. In energy balance problems, calculating sensible heat helps determine how much energy must be added to the system to reach a desired temperature change.

Exergy

Exergy is a thermodynamic measure of the maximum useful work that can be extracted from a system as it comes into equilibrium with a defined reference environment. Unlike energy, exergy accounts for the quality and potential of energy to do work. It helps in evaluating how much of the energy input can actually be converted into work.

Transcript

00:01 Let's say that i have an egg, which for some reason you can reasonably approximate to be a sphere.

00:10 And so i have this egg, which we're going to approximate as a sphere with a diameter of 5 .5 centimeters.

00:24 So we're going to say this is diameter 5 .5 centimeters.

00:31 It's originally at a temperature t not of 8 degrees celsius.

00:39 And then i take it and i drop it in this boiling pot of water where it's boiling at 97 degrees celsius.

00:58 And one thing i forgot to say is that the heat capacity of an egg can be assumed to be constant at 3 .32 kilojoules per kilogram.

01:11 Okay, that's just that's the specific heat capacity.

01:16 All right.

01:17 One more thing about this egg is that let's say eggs have a density of 1020 kilograms per meter cubed.

01:29 Okay, now what we want to know is essentially how much heat is transferred to the egg on average.

01:41 And second, what is the destruction? what is the irreversible energy involved in this scenario? okay.

01:53 So for the first part, it's not too bad.

01:56 We know that q is going to be equal to basically.

02:00 Mc delta t, which we can just apply here, except the mass of the egg is not exactly known.

02:08 But we do know that c is constant, so we don't have to worry about integrating this.

02:15 And then this is going to be multiplied by the temperature range, which if we're asking how much heat it will take to go from this temperature to this temperature, then we definitely know the temperature range.

02:28 So let's just say, delta t for now because we need to figure out how to write this mass in terms of what we were given, which is the density, but we know that density times volume is equal to mass.

02:43 And since we assume that this is a sphere, we can say that the mass is going to be equal to the density times four thirds pi r cubed.

02:53 And we know what r is because we know what d is.

02:59 So if we keep, cube r, and we're using the density instead.

03:03 We know that diameter is twice as much as radius.

03:09 So if we're going to cube radius, we need to cube a factor of one half here.

03:15 So this is our mass.

03:17 We know that this temperature range is going to be 97 to 8, which when we're taking a subtraction of celsius, it's basically the same as a subtraction in kelvin...

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