# I Temp and Pressure measure of KE(average)

#### Zahid Iftikhar

Hi
My question is related to interpretation of temperature and pressure in gases on the basis of kinetic molecular theory.
According to it, both temperature and pressure are proportional to average translational kinetic energy of the gas molecules.
Now in a situation where an ideal gas in confined in a cylinder and is heated and it is an isothermal process i.e the temperature is kept constant. How is it possible to increase the pressure according to above stated rule. Now if temperature is constant, average KE should be constant which also determines the pressure. Where I am confused is , if average KE is constant, both temperature and pressure should be simultaneously constant. One of them can't be kept constant while the other changes.
Regards
Zahid

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#### russ_watters

Mentor
Hi
My question is related to interpretation of temperature and pressure in gases on the basis of kinetic molecular theory.
According to it, both temperature and pressure are proportional to average translational kinetic energy of the gas molecules.
Now in a situation where an ideal gas in confined in a cylinder and is heated and it is an isothermal process i.e the temperature is kept constant. How is it possible to increase the pressure according to above stated rule. Now if temperature is constant, average KE should be constant which also determines the pressure. Where I am confused is , if average KE is constant, both temperature and pressure should be simultaneously constant. One of them can't be kept constant while the other changes.
Regards
Zahid
The process you are describing does not exist or rather is overconstrained. Isothermal heating is accompanied by expansion:
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/isoth.html

#### BvU

Homework Helper
It's difficult to heat something while keeping the temperature constant ...
 ah .. too late.

#### Zahid Iftikhar

The process you are describing does not exist or rather is overconstrained. Isothermal heating is accompanied by expansion:
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/isoth.html
The process you are describing does not exist or rather is overconstrained. Isothermal heating is accompanied by expansion:
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/isoth.html
Yes it is isothermal expansion process. The cylinder I mentioned is fitted with frictionless piston and it moves up with more heat added to the working substance and hence does work. My question relates to keeping temperature constant and increasing the pressure. As average KE determines both the temperature and the pressure, how is it possible to change one and fix other.
Zahid

#### BvU

Homework Helper
The cylinder I mentioned is fitted with frictionless piston
Nice to know... And @russ_watters' link says it all: Q=W

#### nasu

The pressure depends on the average KE but not only on it. If you look up the actual formula, it depends on the density of the gas too (number density, n, for example). So as the gas expands n decreases and so does the pressure. At unchanged average KE per molecule.

#### Zahid Iftikhar

The pressure depends on the average KE but not only on it. If you look up the actual formula, it depends on the density of the gas too (number density, n, for example). So as the gas expands n decreases and so does the pressure. At unchanged average KE per molecule.[/QUOTE
Yes, that is the point I am missing. The density does play a role in it as it does not remain constant.
Thanks.

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