Making lce You place 0.410 kg of cold water inside a freezer that has a constant temperature of

step 1 Hello everyone. This is problem 85 from chapter 18. It says you place some amount of cold water

Making lce You place 0.410 kg of cold water inside a freezer...

Making lce You place 0.410 $\mathrm{kg}$ of cold water inside a freezer that has a constant temperature of $0^{\circ} \mathrm{C}$ . The water eventually freezes and becomes ice at $0^{\circ} \mathrm{C}$ (a) What is the change in entropy of the water as it turns into ice? (See Table $17-4$ for the appropriate latent heat.) (b) If the coefficient of performance of the freezer is $4.50,$ how much heat does the freezer exhaust into your kitchen as a result of freezing the water? (c) If your kitchen temperature is $22^{\circ} \mathrm{C}$ , what is the increase in entropy of your kitchen? (d) What is the change in entropy of the universe during the freezing process?

Making lce You place 0.410 $\mathrm{kg}$ of cold water inside a freezer that has a constant temperature of $0^{\circ} \mathrm{C}$ . The water eventually freezes
and becomes ice at $0^{\circ} \mathrm{C}$ (a) What is the change in entropy of the
water as it turns into ice? (See Table $17-4$ for the appropriate latent
heat.) (b) If the coefficient of performance of the freezer is $4.50,$ how much heat does the freezer exhaust into your kitchen as a result
of freezing the water? (c) If your kitchen temperature is $22^{\circ} \mathrm{C}$ , what
is the increase in entropy of your kitchen? (d) What is the change
in entropy of the universe during the freezing process?

Key Concepts

Irreversibility in Thermodynamic Processes

Real-world processes, including refrigeration, are generally irreversible. This irreversibility means that there is always some net increase in the total entropy of the universe during the process, even if the system itself experiences a decrease in entropy during a phase transition.

Heat Transfer in Refrigeration Processes

Heat transfer in refrigeration involves the removal of thermal energy from the cold reservoir (e.g., the freezer) and the rejection of that energy into the warmer surroundings (e.g., the kitchen). Understanding this transfer is essential for determining the impact on the entropy of both the system being cooled and its environment.

Second Law of Thermodynamics and Entropy of the Universe

This principle states that the total entropy of an isolated system, such as the universe, can never decrease over time. In the context of real processes like freezing, while the local entropy of the system (water turning into ice) may decrease, there is a compensating increase in the entropy of the surroundings, leading to an overall increase in the entropy of the universe.

Latent Heat

Latent heat refers to the amount of energy per unit mass required for a substance to undergo a phase change without a change in temperature. In the context of freezing water, it is the energy released when water transforms into ice, and it plays a crucial role in calculating the entropy change during the phase transition.

Coefficient of Performance (COP) for Refrigerators

The coefficient of performance is a measure of the efficiency of a refrigeration system. It is defined as the ratio of the amount of heat removed from the refrigerated space to the work input required to remove that heat. The COP helps in quantifying how much additional energy (in the form of heat) is expelled into the surroundings as a byproduct of the refrigeration process.

Entropy Change in Phase Transitions

This concept involves calculating the change in entropy when a substance undergoes a phase transition, such as freezing or melting, at a constant temperature. The change is determined using the formula ?S = Q/T, where Q is the latent heat released or absorbed during the transition and T is the absolute temperature at which the process occurs.

Transcript

0:00 Hello everyone.

00:01 This is problem 85 from chapter 18.

00:04 It says you place some amount of cold water inside a freezer.

00:08 It's constant at zero degrees celsius.

00:11 This is the water freezes and becomes ice.

00:13 It first asks, what is the change in entropy of the water as it turns into ice? okay, so for this part, remember that equation for q, we usually have mc delta t if we're changing temperature, but here we're not changing temperature.

00:28 We're actually just changing a phase.

00:31 So in order to change phase, you need to multiply m by the latent heat of fusion in this case, because we're going from a liquid to a solid.

00:43 So note that if we're actually talking about the heat going into the system here, heat is actually not leaving the system, so i'm going to put a negative sign there.

00:57 And then if we want the change in entropy, we need to use this queue, because change in entropy is q over t.

01:07 And notice here that this t isn't zero.

01:09 It's 273 because it always needs to be in kelvin.

01:13 Okay, so you might be a bit confused if you try to put in 0 degrees celsius here, you'll get infinity.

01:20 That doesn't make sense.

01:21 So this should be 273 kelvin.

01:24 And using the q from before, so this is just negative mlf over t.

01:32 Putting in all these values, we get approximately negative 503 joules per kelvin.

01:41 So then in part b it asks if the coefficient of performance is 4 .5, how much heat does the freezer exhaust into your kitchen as a result of freezing the water? okay, so if we want to find the heat exhausted, heat exhausted is qh, and that's equal to qc plus w.

02:10 W, we don't know, but qc we do know, because that's actually this, and that we got from part a.

02:24 And so we don't know what w is, but we do know that coefficient of performance is something that was given to us, and it's equal to qc over w.

02:38 And so using this, qc plus qc over the coefficient of performance...

Please give Ace some feedback