Why is it colder at the top of a mountain despite being closer to the sun ?
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The difference in distance to the sun it irrelevant. The sun is around 150 million km from you so any mountain is a legible
Earth radius is 6,371 km so on the equator on the equinox you get 6371 km closer to the sun from sunrise to noon, which takes 6 hours, then the same distance faster away until sunset.
Mount Everest is just under 9 km tall so even if it was on the equator it will be close to the sun for a short part of the. A ravine calculation of how long part of the day the peek is close to the sun compared to where it is noon is 9/6371 * 6 * 60*2 =1 minute The speed you move towards and away from the sun is not constant, I remember doing it in the past and the answer was around 8 minutes. You do not feel an enormous change in the heat from the sun in an 8 minutes period around noon so the distance effect is not relevant.
Mountains are cooler because the pressure is lower. A gas that expands cools down in temperature so when air is raised up the temperature gets lower. The sunlight will heat up the ground at the same rate at high altitudes but it will be surrounded by cooler air so the net effect is that it is cooler.
If you use a spray bottle you will feel that it and the nozzle get cool when you use it. That is because the high-pressure gas in it expands and cools down
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