Heating a room and internal energy question

[sbdavinci]

Hi, I am having a hard time answering this question. Any help will be appreciated.
In 1938, the journal Nature published a paper by R. Emden titled “Why do we have winter heating?” (Nature Vol 141 pp. 908-9 – although you do not need to read it to answer the problem). This article asserts that heating a room does not increase the total internal energy of the room. Examine this assertion assuming:

(a) the room is filled with an ideal gas
(b) the volume of the room is fixed
(c) the pressure of the room is variable and set by the external atmosphere.
(i) Show that the internal energy of the room is independent of the temperature of the room!
(ii) What state variables change with temperature in order to maintain constant internal energy? How are they affected by temperature (derive an equation to describe this)?

Thank you

 

[stockzahn]

Based on the assumptions for constant values in the statement: If you rearrange the ideal gas equation to substitute the variable terms in the formula for internal energy, maybe you are able to see how the internal energy changes with varying temperature.

 

[Chestermiller]

If the temperature rises by ΔT, what is the change in the internal energy per mole? If the temperature rises by ΔT, what is the change in the number of moles of gas in the room?

Chet