Video: Knowing the Units for Physical Quantities

Which of the following is the correct unit for the specific latent heat of fusion? [A] J⋅kg/°C [B] kg/J [C] J/kg⋅°C [D] J/kg [E] J⋅kg.

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Video Transcript

Which of the following is the correct unit for the specific latent heat of fusion? 1) Joules kilograms per degrees Celsius 2) Kilograms per joule 3) Joules per kilogram degrees Celsius 4) Joules per kilogram 5) Joules kilogram.

Okay, so in this question we’re trying to find the correct unit for the specific latent heat of fusion. So what does the specific latent heat of fusion actually mean? Well, we can break this phrase down into two chunks. Firstly, specific and secondly, latent heat of fusion. Now, this might not look like the most even way of dividing the phrase up. But this is how we want to be doing it. Because firstly, the word specific means per unit mass. In other words, the specific latent heat of fusion is the latent heat of fusion per unit mass.

What it doesn’t mean is how we would use the word specific in every language. It doesn’t mean particular latent heat of fusion. And it’s worth knowing the fact that specific means per unit mass because it does pop-up every so often in physics. For example, we’ve got the specific latent heat of fusion, the specific latent heat of vaporization, the specific heat capacity. All of these are quantities per unit mass.

So coming back to the latent heat of fusion then, what is the latent heat of fusion? Well, the latent heat of fusion is the energy needed to change a solid, at its melting point, entirely into a liquid. In other words, let’s say we’ve got a block of stuff. It doesn’t matter what the stuff is. But it’s in a solid state. Here is our block. Now, we bring this block up to its melting point. From this point on, we’re converting this solid into a liquid, a really badly-drawn liquid. But this process requires energy. We need to put in energy to convert that solid into a liquid. And the latent heat of fusion is the amount of energy that we need to put in to convert that solid entirely into a liquid.

So let’s say that this solid is, for example, 10 kilograms of stuff. Well, you need a certain amount of energy to convert all of it into a liquid. But you only need one-tenth of that energy because we’ve got 10 kilograms to convert one kilogram of that solid into liquid. Remember, one kilogram of solid into one kilogram of liquid. And that is the specific latent heat of fusion. Because if we’re talking about just latent heat of fusion, then it can apply to any substance and any mass of that substance. However, the specific latent heat of fusion is the amount of energy needed per unit mass to convert that solid entirely into a liquid.

In other words, how much energy do we need to convert one kilogram of that stuff into a liquid? So as an equation, we can write, the specific latent heat of fusion, 𝐿, is equal to the energy needed per unit mass to convert that solid into a liquid. And so the specific latent heat of fusion is going to have units of joules, because energy has a unit of joules, per kilogram, because mass has a unit of kilograms. At which point, we can look at the numbers one to five and see which one matches joules per kilogram. Well, it’s number four. So the correct unit for the specific latent heat of fusion is joules per kilogram.

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