Pressure and temperature -- the effects of one upon the other

[cGibson]

Greetings,

I get that increased temperature increases pressure. But does increased pressure increase temperature. For example: 1) If I press down on a table with a heavy object, does it increase its temperature. 2) Or does the pressure of the crust and the mantle of the Earth, contribute to the increase of the temperature of the core?

Thanks!

 

[jbriggs444]

I get that increased temperature increases pressure. But does increased pressure increase temperature. For example: 1) If I press down on a table with a heavy object, does it increase its temperature. 2) Or does the pressure of the crust and the mantle of the Earth, contribute to the increase of the temperature of the core?

You should probably discard the idea of cause and effect here. It is not necessary and is a hindrance to understanding.

All other things being equal, there is a correlation between pressure and temperature in an ideal gas. If temperature is higher, pressure must be higher. If pressure is higher, temperature must be higher. It is not required that the increase in temperature caused the increase in pressure. It is not required that the increase in pressure caused the increase in temperature. It is enough that when given an increase in one you can calculate the increase in the other.

It is the same way with force and acceleration and f=ma. It does not matter whether the force of your hand on a ball causes an acceleration or whether the acceleration of a car causes a force of the seat on your posterior. It is enough that you can calculate either one when given the other.

 

[mfig]

I get that increased temperature increases pressure. But does increased pressure increase temperature.

First, it is not necessarily true that increased temperature means an increase in pressure. It depends on the equation of state for the material. For example, if we use the ideal gas law as our EoS then we know that

$pV = mRT$

And so we see that if the temperature of a fixed mass of gas goes up the product of the pressure and volume must go up. It could be that the volume goes up and the pressure is fixed, or the other way around.

You can find EoSs for solids if you look within the fields of geology and mineralogy. Once you examine these, you should be able to predict how increasing temperature impacts pressure and vice versa.