[QUE/TH-05003] TH-PROBLEM

Consider $n$ mole of ideal gas whose entropy is given by $$ \frac{n}{2}\left[c_1\,+\,5R{\ln}\frac{U}{n}\,+\,2R{\ln}\frac{V}{n} \right]$$ where $R$ is the univeral gas constant, $U$ the internal energy, $V$ the volume and $c_1$ a constant.

• Calculate the specific heats $c_V$ and $c_p$
• A room is at a temperature $273^o$ K which is in equilbrium with the surroundings. One hour after turning on a heater, the room is at $300^o$ K. Assuming the air is described by the equation given above, find the energy density for the two different temperatures. Answer should be in terms of the atmospheric pressure $P_0$, assume it is constant and the room is always at $P_0$.