Question

why does lower internal energy mean lower temperature of a real gas? couldn't just the potential energy decrease and not temperature? If there is a proof mathematically please show.

Answer 1

Heat means only the energy of molecular motion that is transported through the gas from the region of higher temperature to the region of lower temperature. Thus heat denotes the energy flow under influence of a temperature difference. On the other hand ,internal energy of a gas is equal to the collective energy possessed by its molecule in the random motion.

(I) In an actual gas, the molecules attract each other and on the account of this , they causes potential energy (Ep)which is negative in sign*. * Denotes attractive forces give rise to negative potential energy and repulsive forces give rise to positive potential energy .

On account of their motion , the molecules possess kinetic energy (Ek) . Thus the internal energy (U) of an actual gas is the sum of both of these types of energy that is

U = Ek + Ep

Now , when an actual gas expands, work is done in pulling the molecules apart against the attractive intermolecular forces . As a result of this, the potential energy of the gas molecules increases thereby increasing the internal energy . Thus in case of an actual gas ,the internal energy depends not only on its temperature but also on its volume. When Such a gas expands without using external work and without allowing any heat to enter or leave it during the expansion, its total potential energy increases but according to the law of conservation of energy , the sum of the potential energy and kinetic energy of all the molecules is to remain constant .Obviously the kinetic energy decreases. A decrease in kinetic energy will result in fall in the temperature of the gas . This effect in which cooling is caused by the control expansion of gas is called Joule Thomson effect.

(II) In case in case of an ideal gas, there are no attractive intermolecular forces between its molecule . Thus, whenever such a gas expands, no work is done to overcome these forces . In other words, the potential energy of the molecules of an ideal gas is zero , that is

Ep=0

Thus , U=Ek

Obviously,the internal energy of an ideal gas is wholly Kinetic. Since kinetic energy is dependent only on the temperature and not on the volume of the gas, it follows that:

"Internal energy of an ideal gas depends only upon its temperature and is independent of its volume."