De la vapeur d'eau (54 g), maintenue à 373 K, est introduite dans un mélange d'eau (900 g) et

De la vapeur d'eau (54 g), maintenue à 373 K, est...

De la vapeur d'eau $(54 \mathrm{~g})$, maintenue à $373 \mathrm{~K}$, est introduite dans un mélange d'eau $(900 \mathrm{~g})$ et de glace $(90 \mathrm{~g})$, en équilibre à $0{ }^{\circ} \mathrm{C}$. Que se passe-t-il ? Lorsque l'équilibre final est atteint, y a-t-il encore de la glace? Quelle est alors la température de l'eau ?

De la vapeur d'eau $(54 \mathrm{~g})$, maintenue à $373 \mathrm{~K}$, est introduite dans un mélange d'eau $(900 \mathrm{~g})$ et de glace $(90 \mathrm{~g})$, en équilibre à $0{ }^{\circ} \mathrm{C}$.
Que se passe-t-il ? Lorsque l'équilibre final est atteint, y a-t-il encore de la glace? Quelle est alors la température de l'eau ?

Key Concepts

Latent Heat of Vaporization

This is the energy required to convert a substance from a liquid to a vapor without changing its temperature. In thermodynamic problems involving steam condensation and subsequent energy transfer, latent heat of vaporization determines how much energy is released when vapor condenses to liquid, which in turn affects the temperature and phase changes in the system.

Latent Heat of Fusion

This is the energy needed to change a solid into a liquid (or vice versa), at constant temperature. It is critical for determining how much ice can melt when energy is transferred between phases, as well as balancing energy exchanges in mixtures involving the melting of ice.

Phase Equilibrium

Phase equilibrium refers to the state where different phases of a substance (such as ice and water) coexist at a specific temperature and pressure with no net change in the amount of each phase. In problems involving mixtures of ice and water, phase equilibrium conditions (often at 0°C for water) constrain the final temperature and state distribution.

Energy Conservation in Phase Changes

This principle involves equating the energy released or absorbed during phase transitions to the energy required for temperature changes. In scenarios where phase changes (condensation, freezing, melting) occur, energy conservation is applied to ensure that the total energy before and after the process remains constant, helping to determine the final state of the system.

Heat Transfer between Substances with Different Phases

Heat transfer is the process of energy exchange between substances at different temperatures and phases, such as when hot vapor is introduced into a mix of ice and water. Understanding the transfer of heat between phases is essential in predicting whether the system's final state will involve phase change, like the presence or absence of remaining ice, and what the final temperature will be.

Transcript

00:01 For this question we have a calorie meter containing 200 grams of steam which is at 150 degrees celsius and also 100 gram of ice that is at 40 degrees celsius we are to find after mixing both of these things together what is the final temperature and how much steam ice or water are present.

00:32 Now to start off we have three different possible scenarios.

00:39 So three scenarios.

00:42 The first scenario is that we have steam.

00:49 All the ice has melted and enough energy, there's enough energy to actually boil the ice all the way to 100 degrees, such that they become steam as well.

01:06 So everything is steam.

01:10 On the other hand, the other case would be everything is ice.

01:17 Right, the amount of ice is enough to bring the steam down all the way to liquid and then to freeze it.

01:28 And finally, the third case is both the steam and the ice.

01:34 As they lose energy or they gain energy, they become water and then there's a mixture of water and ice or water and steep right water at 100 degrees which is with steam or water at zero degrees or water in between so the first two cases is most likely improbable and the reason is because their masses are pretty much very similar so not there's no favourable no favorable condition that is actually much over like over weighing the other other components like this it's not like there's like 10 or 20 times amount of steam compared to ice right that that would be a possible case where everything will turn to steam right that's not the case because they have quite similar amount of mass so we can get rid of these two different possibilities the other possibility would be having a mixture of water and steam or water and ice or something in between so to find out which one of these cases is true we want to first find what is the amount of energy required to completely melt the ice and what is the amount of energy required to completely convert the steam into water.

03:27 It will become clear later why we are doing this, but we're going to calculate that first.

03:33 So the energy required to convert steam to 100 degrees celsius water.

03:43 The steam at 150 degrees celsius to 100 degrees water.

03:50 This will be taking the mass.

03:58 Multiply by the heat capacity of steam.

04:07 Multiply by the change in temperature, which is 50 degrees.

04:13 Then we add the latent heat of vaporization because you want to convert from steam to liquid.

04:21 So we have 0 .2 kilograms multiplied by 2256 kilojoules.

04:45 So this 466 .4 kilojoules.

04:51 Now to look at the amount of energy, required to convert from negative 40 degrees ice to 0 degrees celsius water so we first have we know the mass of the ice is 100 gram 2 .1 kilograms multiplied by heat capacity of ice which is 2 .090 change in temperature is 40 degrees let me add latent heat of fusion which is 334...

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