if hot air rises why is it cooler at the top of mountain than near sea level?

The drop in temperature at the top of mountains is because of the change in Atmospheric Pressure. We all know the relationship between pressure and temperature. Both Pressure and Temperature vary proportionally. This is what Thermodynamics says. But I hate equations and formulas. Let's have a practical explanation and good understanding of this.

There are two factors why there is a drop in temperature at the top of mountains.
1. Drop in Pressure
2. The Amount of water vapour in the air. 

1) Drop in pressure
The cause of the atmospheric pressure will let us know the reason for this fall in Pressure with an increase in Altitude. The word pressure is the extension of the word press. The surface of our earth is pressed up by the air present above the Surface because we know that air has mass and so it is pulled down to the Surface by gravity. The Weight of the Air acts all over the Surface and exerts a pressure ( a force). This pressure is atmospheric pressure.

Gravity plays an important role in this. Gravity is maximum at sea level and it decreases when we move up. Above a mountain, the Gravity decreases so the Atmospheric Pressure decreases.

The Drop in Pressure decreases temperature. This is because when the pressure increases, more number of particles or molecules are contained in the space. Every particle possesses some Heat. When the number is more, the heat possessed by all the particles together is more. Also, the collisions between these molecules are more which produces heat. When Pressure decreases, the molecules spread out and so the heat is not concentrated so the temperature goes down.

2) The Amount of water vapour in air

Water Vapour constitutes 36-70% of Greenhouse gases. Water Vapours absorb heat from the sun and make the surrounding warm. This is at ground level. At Higher Altitudes, these water vapours condense due to the decrease in Pressure and form mist which are suspended water particles. The water vapour present at top of the mountain is less so there is less absorption of heat from the sun which prevents the rise of temperature.