Answer to Question #180704 in Physical Chemistry for Mike Chow

Question

5a) What is change in the internal energy E for an ideal gas if its volume changes at constant temperature?

5b) What can you say about the change in the internal energy E for a real gas in which the gas molecules repel each other as its volume changes at constant temperature?

5c) For the gases in parts a and b, what can you say about the change in their internal energy E when the temperature is changed at constant volume?

Answer 1

a) If you keep the volume constant then the gas can do no work as δW=PΔV=0 and so from the first law of thermodynamics the change in internal energy.

b) We just concluded that the internal energy for an ideal gas equals the kinetic energy, and it is therefore a function of the temperature of the gas, but not its density. Now, we know that ideal gases are simplified representations of real gases, but they do not exist.

c) Pressure and volume change while the temperature remains constant. Since no work or heat are exchanged with the surrounding, the internal energy will not change during this process. Thus, the internal energy of an ideal gas is only a function of its temperature.