The 2010 Nobel Prize in Physics was awarded for the discovery of graphene, a two-dimensional form of carbon in which the atoms form a two-dimensional crystal-lattice sheet only one atom thick. Predict the molar specific heat of graphene. Give your answer as a multiple of R.

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Accepted Answer

Hey, everyone. Let's go through this practice problem. Black phosphorus is a two dimensional material made of phosphorus atoms arranged in a layered structure. Black phosphorus is one or a few atoms layered thick material. It has unique electronic and optical properties express the molar specific heat of black phosphorus as a multiple of the universal gas constant R, we have four multiple choice options. Option A, the R divided by two option D R, option C two R and option D four R. Now this problem fortunately is not too hard because there is a simple relationship here at work where the molar specific heat for a molecule is equal to one half multiplied by the number of degrees of freedom for the molecule multiplied by the ideal gas constant. In order for this equation to work, though, we need to first determine the number of degrees of freedom. So the problem tells us that we're looking at a two dimensional material which means that it can move, it can translate along the x axis or the y axis, two different axis. So there are going to be two degrees of freedom from that. But of course, it can also rotate. So there's at least one more degree of freedom from rotational motion. But then there's also the fact that the problem doesn't specify that it is a rigid structure. There's going to be one more degree of freedom because we don't know if there could be a stretching or vibrational motion. So in total, there are four degrees of freedom for this problem. So all we have to do is plug this in for D. So one half multiplied by four R or in other words, QR So two is then the answer to the problem and that's really it. And then if you look at the multiple choice options, option C agrees with this answer. So option C is the answer to this problem and that's all for this video. I hope it helps you out. If you need more practice, please check out some of our other videos which will give you more experience with these types of problems. But that's all for now. I hope you all have a lovely day. Bye bye.

The 2010 Nobel Prize in Physics was awarded for the discovery of graphene, a two-dimensional form of carbon in which the atoms form a two-dimensional crystal-lattice sheet only one atom thick. Predict the molar specific heat of graphene. Give your answer as a multiple of R.

Verified Solution

Key Concepts

Graphene Structure

Molar Specific Heat

Debye Model