At room temperature, butter softens but remains solid. It melts at 90F, which is above what most consider room temperature.
As to why, well, butter is mostly made of saturated fat. Saturated fats are solids at room temperature due to the way the molecules are structured – they can stack more densely, which makes it harder for them to spread out like liquids.
As to why other dairy products aren’t solid at room temperatures, it has to do with the type of emulsions they are. Milk and cream are fats dispersed in water, and water is liquid at room temperatures. Butter is the opposite – it’s water dispersed in saturated fat, which is solid.
It’s not that it’s dairy. It’s that it is fat. Have you ever made bacon? Lots of people store bacon grease to cook with later, and it does a lot of similar kinds of changes in consistency too. It’s also why other things like margarine (which is made of fatty oil) works like a butter substitute.
And even then, not all fats do it. Just the ones with lots of hydrogen in them. In fact thats why those fats are called saturated fats. What they are saturated with is hydrogen.
Whether molecules are solid, liquid or gas depends on how they interact with one another (intermolecular forces or IMFs). Butter is mostly a form of fat called a triglyceride. The longish (18 atom) carbon chains like hanging around with each other so the IMFs are very high. This makes the butter solid.
We don’t see this in something like milk because the fats are a lot more spread out (dispersed) in water so we don’t get lots of them hanging out together until the milk goes bad and the fats and water separate.
/u/Vadered has the right explanation but I’d like to expand a bit.
Saturated fats are long straight chains, so they will stack together nicely like a box of crayons.
Unsaturated fats have one or more double bonds and they put a kink in the chain so that they will no longer stack nicely together, and that keeps them liquid.
Saturated fats are solids at room temperature.
Monounsaturated fats – like olive oil – are liquid at room temperature but solid in the fridge.
Polyunsaturated fats are liquids and room temperature and in the fridge.
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