Video: Understanding Specific Latent Heat

1 kg of copper and 1 kg of nickel are both heated continuously at the same rate. Determine which metal will completely melt first. Use a value of 205 kJ/kg for the specific latent heat of fusion of copper and use a value of 297 kJ/kg for the specific latent heat of fusion of nickel.

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Video Transcript

One kilogram of copper and one kilogram of nickel are both heated continuously at the same rate. Determine which metal will completely melt first. Use a value of 205 kilojoules per kilogram for the specific latent heat of fusion of copper and use the value of 297 kilojoules per kilogram for the specific latent heat of fusion of nickel.

Okay, so we’ve got blocks of one kilogram of copper and one kilogram of nickel. In other words, we’ve got the same amount of both metals: one kilogram and one kilogram. Both of these blocks are heated continuously at the same rate. Basically, what that means is that the same amount of energy is supplied to them every second because as we heat them, we supply energy to them. If they’re heated continuously, then they’re constantly being heated without the heating stopping. And if they’re being heated at the same rate, then we’re supplying the same amount of energy to each block for a given unit of time.

We are given the specific latent heat of fusions for copper and for nickel. It’s 205 for copper and 297 for nickel. This is the key to solving our problem but we need to know what specific latent heat of fusion actually means. Let’s break down this rather long and complicated phrase, starting with specific.

Specific in this context means per unit mass. It doesn’t mean a very particular latent heat of fusion, but specific instead means per unit mass. In other words, it’s the latent heat of fusion per unit mass — the latent heat of fusion of a substance for every one kilogram of that substance. And we can see this in the units of specific latent heat of fusion. It’s kilojoules per kilogram- per kilogram. So that’s what specific means.

But what does latent heat of fusion mean? Well, let’s work with latent heat next. Latent heat is simply the energy needed to change state without a change in temperature. That W slash O basically just means without. In other words, latent heat is the amount of energy we need to supply to a substance in order for it to change state from maybe a solid to a liquid or a liquid to a gas or vice versa without changing the temperature of the substance.

And we can see this in the units as well. It’s given in units of kilojoules which are units of energy. And finally, latent heat of fusion, this just refers to the solid to liquid transition. So the specific latent heat of fusion is the energy needed to change from a solid to a liquid without a change in temperature per unit mass.

Yeah, that is a lot to handle. But don’t worry, we can work through this problem. Let’s now start considering the copper and nickel blocks that we’ve been given. Well, we’ve been given one kilogram of them both. So we’ve got the same amount of stuff for each one of them, which means that if the masses are equal, then we can just compare the amount of energy it takes to melt these blocks. And that is exactly what we’re doing because we’ve got the specific latent heat of fusion. We are melting these blocks from solid to liquid.

Now, we know that copper takes 205 kilojoules to melt one kilogram of copper from solid to liquid without changing its temperature. Nickel however needs 297 kilojoules. We said earlier that both are being heated continuously and at the same rate. So 205 kilojoules will be supplied to the copper quicker than 297 kilojoules will be supplied to the nickel.

Obviously, both blocks have the same amount of energy supplied to it in the same amount of time. So which will be supplied quicker: 205 kilojoules or 297 kilojoules? Obviously, 205 kilojoules will be supplied quicker because this is a smaller value.

In other words, the block of copper will melt completely before the block of nickel will. And so our final answer is that the copper will completely melt first.

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