A copper calorimeter can with mass 0.446 kg contains 0.0950 kg of ice. The system is initially a

A copper calorimeter can with mass 0.446 kg contains 0.0950...

Key Concepts

Conservation of Energy

This concept involves the principle that energy cannot be created or destroyed, only transferred. In calorimetry, the heat lost by the warmer component (for example, the steam condensing or cooling) is equal to the heat gained by the colder components (such as melting ice or warming the calorimeter), ensuring that the overall energy in the system remains constant.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius or Kelvin. It is critical in calculating the temperature change when heat is added or removed and is used for both solids and liquids in calorimetric problems.

Latent Heat of Fusion and Vaporization

Latent heat refers to the energy required to change the phase of a substance without changing its temperature. The latent heat of fusion is used during the process of melting ice into water, while the latent heat of vaporization is relevant for the condensation of steam into liquid water. These values are essential for determining the energy exchange during phase transitions.

Phase Changes

Phase changes involve transitions between solid, liquid, and gas states. During these transitions, the material absorbs or releases latent heat without a change in temperature. Understanding phase changes is crucial when dealing with mixtures of ice, water, and steam in calorimetry problems.

Thermal Equilibrium

Thermal equilibrium is the state in which all parts of a system have reached a uniform temperature and no further heat exchange occurs. This concept is central to calorimetry problems, where the final temperature of the system is found by setting the net heat transfer to zero as the system reaches equilibrium.

Transcript

00:01 All right, in this question we're going to do some calorimetry with steam being added to a copper container with some ice in it and we're going to find the final temperature of the mixture and then how much ice steam and liquid water there is at the end.

00:17 So what helps me with calorimetry is this graph that you see which you can you have seen it possibly as temperature versus time or temperature versus heat, either one.

00:33 And this graph shows and since we're using water i labeled the temperature zero degrees celsius and 100 degrees celsius on that y -axis.

00:42 So our first slope segment shows the solid phase, the second slope segment shows the liquid phase, and then the third slope segment over here shows the gas phase.

00:54 And what we're indicating here is that as we add heat we get an increase in temperature.

01:00 So we start off with a solid that's below the freezing point, we add some thermal energy and we bring it to its melting slash freezing point.

01:08 So this horizontal segment will be melting if we're going one way or freezing if we're going the other way.

01:15 If we are adding heat we're going to be melting it.

01:18 If we're removing heat we're going to be freezing the substance.

01:22 And then once we've melted or frozen, well once we've melted everything, then our liquid can warm up and then we're going to reach the point where we are either boiling, so for water that's 100 degrees celsius, or we are condensing.

01:39 So that's our phase change and likewise melting versus freezing is also phase change.

01:44 So we have to take all of our liquid water and evaporate or boil away all of it into gas, into steam, before we can then change the temperature of the gas phase.

01:56 And what i like to do with calorimetry questions, i'm just going to focus on the water, well sorry the ice and the steam at the moment, is that we'll mark the fact that we are starting off with ice at zero degrees.

02:12 So it's still solid but it's at zero degrees.

02:16 So you know here's our ice and then we have steam at 100 degrees and so our steam is starting here.

02:25 And what's going to happen in this process is the ice is going to first of all all melt and then it's going to be able to warm up to some final temperature.

02:45 I'm going to call it just t actually, not t final.

02:48 Well at the same time our steam is going to condense and lose energy and then the water that condenses out of that is likewise going to, you know let's actually do that in a different color, let's choose like blue here.

03:07 So our steam is going to lose energy and then our water from that is going to lose energy and we're going to have like i said that temperature t of the final mixture.

03:21 Now this question we have to worry about the copper container as well.

03:24 And the way i approach this question was to assume that we're going to assume that all the steam condenses into liquid water and therefore gives up all of its energy into first melting the ice and then warming up the copper container and the cold water.

04:12 And then we'll also have the hot water that condensed out of the steam losing some energy as well.

04:19 So i broke this down into exactly that.

04:23 I said let's figure out how much steam has to condense or like how much energy does the steam give up to melt the ice.

04:56 And then i found how much energy is left over after that to warm up the copper and the cold water.

05:30 And of course you know our steam will have condensed into liquid water in that process.

05:38 So by breaking it down like this i could figure out what's the final temp just from the temperature of the copper and cold water just from the steam condensing.

06:03 And then i could look at which i don't want to put that here.

06:09 So thinking of it this way lets me first of all find the t from the steam condensing and then what's the actual final final temperature from the hot water cooling off and transferring its energy to the copper and cold water.

06:43 So breaking it down this way seemed to make the most sense to me.

06:47 Again our graph only handles mixing the steam and the water.

06:53 So how much energy do we need to melt that ice? so we can find the heat for that with the mass of the ice times the latent heat of fusion.

07:13 And that gives me latent heat of fusion or it might you might also think of it as the energy for melting depending on which way you want to go with it.

07:26 And that is 334 joules per gram.

07:30 So that's 334 times 10 to the third joules per kilogram.

07:38 And i got that it's going to take three thousand sorry 31 ,730 joules to melt the ice.

07:46 Okay great...

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