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We Know, Pressure $\alpha$ Temperature at Constant Volume (Gaylussac's Law).

And Temperature $\alpha$ Kinetic Energy, Does this imply that Kinetic Energy $\alpha$ Pressure or is Directly Proportional To Pressure?

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Comments

Consider this:

A sealed isolated container filled with some amount of gas is present somewhere in space. There is a provision to supply heat to the gas so as to increase its temperature. But other than this, there is no interaction between our system and the environment.

Obviously, the volume of this gas will not change. Now how does one increase the pressure of the gas inside? The only way to do this will be to heat the gas so that its temperature increases. The increase in temperature causes(as you have mentioned) increase in kinetic energy. Basically it means that the gas molecules are now moving faster and hitting the walls of the container at a higher rate. This increased rate of collision is what physically manifests as increase in pressure.

Increase in temperature is the cause, and increase in pressure is the effect. You can increase pressure(while keeping volume and number moles constant) only by increasing the temperature.

Hope this helps.

Raghav Vaidyanathan - 5 years, 11 months ago

We consider the equation P = 1/3 ( density * C r.m.s^2) and prove the same . From your above mentioned example..

Krishna Shankar - 5 years, 11 months ago

@Raghav Vaidyanathan @Nihar Mahajan @Swapnil Das @Sravanth Chebrolu @Sharky Kesa Please Help.

Mehul Arora - 5 years, 11 months ago

Yeah. I agree with Raghav sir. As he said the increase in kinetic energy is caused by the increase in the temperature. And as you said, $\text{temperature}\propto \text{pressure}$ . So, isn't it obvious that $\text{pressure}\propto\text{kinetic energy}$ .

Because the increase in kinetic energy causes the molecules to vibrate more vigorously, causing more collision and indirectly increasing the pressure.

Sravanth C. - 5 years, 11 months ago

Hi, you can post your problem in Chemistry Stack Exchange to get your question being answered soon.

Swapnil Das - 5 years, 11 months ago

@Swapnil Das , It seems that my doubt has already been answered ;)

Mehul Arora - 5 years, 11 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}`	$\boxed{123}$