Why do we feel cold at mountain peaks?

according to the archimedes principle fluids having less density floats on fluids having more density. As hot air has less density than cold air ,so hot air should float on cold air. But in our atmosphere the tempreture decrease as we move in upward direction, but it should increase as hot air should float on cold air. why is it so?

#Physics #HelpMe!

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Temperature does increase as you rise in altitude, but to a certain extent. There hits a point when the temperature starts to decrease (because outer space is cold, simply put). So temperature does increase, but by an insensible amount.

Bob Krueger - 7 years, 8 months ago

but what is that point ? what is the limit of that point?

vyom chaturvedi - 7 years, 4 months ago

Assuming this is an ideal condition, we can apply the ideal gas law for gases

$PV = nRT$ where $P$ is pressure, $V$ is volume, $n$ is the amount in moles, $R$ is the gas constant, $(R = 8.31)$ . And $T$ is the temperature of the air

Expressing this in $T$ will give us $T = \frac{PV}{nR}$ Since pressure and volume of gas both decrease as altitude increases, and amount of gas molecules remains constant, the equation shows that temperature decreases with increasing altitude

Saad Haider - 7 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$