(II) (a) An ice cube of mass m at 0^∘ C is placed in a large 20^∘ C room. Heat flows (from the r

(II) (a) An ice cube of mass m at 0^∘ C is placed in a large...

(II) $(a)$ An ice cube of mass $m$ at $0^{\circ} \mathrm{C}$ is placed in a large $20^{\circ} \mathrm{C}$ room. Heat flows (from the room to the ice cube) such that the ice cube melts and the liquid water warms to $20^{\circ} \mathrm{C} .$ The room is so large that its temperature remains nearly $20^{\circ} \mathrm{C}$ at all times. Calculate the change in entropy for the (water $+$ room $)$ system due to this process. Will this process occur naturally? (b) A mass $m$ of liquid water at $20^{\circ} \mathrm{C}$ is placed in a large $20^{\circ} \mathrm{C}$ room. Heat flows (from the water to the room) such that the liquid water cools to $0^{\circ} \mathrm{C}$ and then freezes into a $0^{\circ} \mathrm{C}$ ice cube. The room is so large that its temperature remains $20^{\circ} \mathrm{C}$ at all times. Calculate the change in entropy for the (water + room) system due to this process. Will this process occur naturally?

(II) $(a)$ An ice cube of mass $m$ at $0^{\circ} \mathrm{C}$ is placed in a large
$20^{\circ} \mathrm{C}$ room. Heat flows (from the room to the ice cube)
such that the ice cube melts and the liquid water warms to
$20^{\circ} \mathrm{C} .$ The room is so large that its temperature remains nearly $20^{\circ} \mathrm{C}$ at all times. Calculate the change in entropy
for the (water $+$ room $)$ system due to this process. Will
this process occur naturally? (b) A mass $m$ of liquid
water at $20^{\circ} \mathrm{C}$ is placed in a large $20^{\circ} \mathrm{C}$ room. Heat flows (from the water to the room) such that the liquid
water cools to $0^{\circ} \mathrm{C}$ and then freezes into a $0^{\circ} \mathrm{C}$ ice
cube. The room is so large that its temperature remains
$20^{\circ} \mathrm{C}$ at all times. Calculate the change in entropy for
the (water + room) system due to this process. Will this
process occur naturally?

Key Concepts

Reversible vs Irreversible Processes

Reversible processes are idealized transformations that occur in infinitesimally small steps and can be reversed without net changes in the system or surroundings. In contrast, irreversible processes, which are more common in nature, lead to an increase in the entropy of the universe. This concept is important for analyzing real-world thermodynamic changes and determining process spontaneity.

Entropy

Entropy is a measure of the disorder or randomness in a system and quantifies the number of microscopic configurations corresponding to a thermodynamic state. When a process occurs, the change in entropy reflects the dispersal of energy and is key to determining whether a process is spontaneous according to the second law of thermodynamics.

Latent Heat

Latent heat is the energy absorbed or released by a substance during a phase change at a constant temperature, such as melting or freezing. It is crucial in processes where substances change phase without a change in temperature, and it must be accounted for when calculating the total energy and entropy changes during such transformations.

Heat Transfer and Temperature Gradients

Heat transfer is the process by which thermal energy moves from a region of higher temperature to a region of lower temperature, often creating temperature gradients. In thermodynamic analyses, understanding heat transfer is essential because it drives changes in the state of matter and influences the overall entropy of the system plus its surroundings.

Second Law of Thermodynamics

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. It provides a criterion for spontaneity in processes, asserting that natural processes tend to increase the overall entropy of the combined system and its environment, and it plays a central role in evaluating and predicting the direction of thermodynamic changes.

Transcript

00:01 The total change in entropy for a given problem in a part a is equal to total change in entropy is equal to the change in entropy during the melting of ice.

00:13 So i will represent it by m melting plus the change in entropy during the warming, which i will represent by w, plus the change in entropy of the room.

00:26 So room in which the ice is melting r so room is represented by r we'll first find a change entropy for melting which is changing entropy for melting is written as using entropy formula that is a q for melting it required for melting over the temperature at which it melts that is equal to qm can be written as m the master latent heat of fusion over tm which is 273 substituting the value of lf then then the change in tropy we get here is a 12 one let us suppose mass is equal to 1 kg so we'll keep it that one therefore i will not write the m so m is assumed to be 1 kg here so this will become 1219 .78 jr.

01:34 Jules per kelvin and the entropy for warming can be written is the integral of dq for warming dq for warming divided by t then taking integration from the temperature of melting to temperature of the room r, then our integration becomes mc, integrant becomes d t over t.

02:14 And evaluating this integral gives us the value which is mc times the l and of temperature of a room divided by temperature for a melting.

02:28 If i substitute the value of for temperature for room and then temperature for melting then the resultant i will get here by substituting a c is 295 .95.

02:44 I still assume the mass to be one here so therefore i will just write this number joules per kelvin and similarly the change in entropy for for a room are that is a to a minus ml, latent heat of fusion minus mc times the change in temperature tr minus tm...

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